SDS-2.2, Scalable Data Science

Archived YouTube video of this live unedited lab-lecture:

Power Plant ML Pipeline Application

This is an end-to-end example of using a number of different machine learning algorithms to solve a supervised regression problem.

Table of Contents

• Step 1: Business Understanding
• Step 2: Load Your Data
• Step 3: Explore Your Data
• Step 4: Visualize Your Data
• Step 5: Data Preparation
• Step 6: Data Modeling
• Step 7: Tuning and Evaluation
• Step 8: Deployment

We are trying to predict power output given a set of readings from various sensors in a gas-fired power generation plant. Power generation is a complex process, and understanding and predicting power output is an important element in managing a plant and its connection to the power grid.

More information about Peaker or Peaking Power Plants can be found on Wikipedia https://en.wikipedia.org/wiki/Peaking*power*plant

Given this business problem, we need to translate it to a Machine Learning task. The ML task is regression since the label (or target) we are trying to predict is numeric.

The example data is provided by UCI at UCI Machine Learning Repository Combined Cycle Power Plant Data Set

You can read the background on the UCI page, but in summary we have collected a number of readings from sensors at a Gas Fired Power Plant

(also called a Peaker Plant) and now we want to use those sensor readings to predict how much power the plant will generate.

More information about Machine Learning with Spark can be found in the Spark MLLib Programming Guide

Please note this example only works with Spark version 1.4 or higher

To Rerun Steps 1-4 done in the notebook at: * Workspace -> scalable-data-science -> sds-2-2 -> 009PowerPlantPipeline01ETLEDA

just run the following command as shown in the cell below:

%run "/scalable-data-science/sds-2-2/009_PowerPlantPipeline_01ETLEDA"

• Note: If you already evaluated the %run ... command above then:
  • first delete the cell by pressing on x on the top-right corner of the cell and
  • revaluate the run command above.

"/scalable-data-science/sds-2-2/009_PowerPlantPipeline_01ETLEDA"

Now we will do the following Steps:

Step 5: Data Preparation,

Step 6: Modeling, and

Step 7: Tuning and Evaluation

Step 8: Deployment

Step 5: Data Preparation

The next step is to prepare the data. Since all of this data is numeric and consistent, this is a simple task for us today.

We will need to convert the predictor features from columns to Feature Vectors using the org.apache.spark.ml.feature.VectorAssembler

The VectorAssembler will be the first step in building our ML pipeline.

//Let's quickly recall the schema
// the table is available
table("power_plant_table").printSchema

root
 |-- AT: double (nullable = true)
 |-- V: double (nullable = true)
 |-- AP: double (nullable = true)
 |-- RH: double (nullable = true)
 |-- PE: double (nullable = true)

//the DataFrame should also be available
powerPlantDF

res22: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]

import org.apache.spark.ml.feature.VectorAssembler

// make a DataFrame called dataset from the table
val dataset = sqlContext.table("power_plant_table") 

val vectorizer =  new VectorAssembler()
                      .setInputCols(Array("AT", "V", "AP", "RH"))
                      .setOutputCol("features")

import org.apache.spark.ml.feature.VectorAssembler
dataset: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
vectorizer: org.apache.spark.ml.feature.VectorAssembler = vecAssembler_00521eb9630e

Step 6: Data Modeling

Now let's model our data to predict what the power output will be given a set of sensor readings

Our first model will be based on simple linear regression since we saw some linear patterns in our data based on the scatter plots during the exploration stage.

Linear Regression Model

• Linear Regression is one of the most useful work-horses of statistical learning
• See Chapter 7 of Kevin Murphy's Machine Learning froma Probabilistic Perspective for a good mathematical and algorithmic introduction.
• You should have already seen Ameet's treatment of the topic from earlier notebook.

Let's open http://spark.apache.org/docs/latest/mllib-linear-methods.html#regression for some details.

// First let's hold out 20% of our data for testing and leave 80% for training
var Array(split20, split80) = dataset.randomSplit(Array(0.20, 0.80), 1800009193L)

split20: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
split80: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]

// Let's cache these datasets for performance
val testSet = split20.cache()
val trainingSet = split80.cache()

testSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
trainingSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]

testSet.count() // action to actually cache

res24: Long = 1966

trainingSet.count() // action to actually cache

res25: Long = 7602

Let's take a few elements of the three DataFrames.

dataset.take(3)

res26: Array[org.apache.spark.sql.Row] = Array([14.96,41.76,1024.07,73.17,463.26], [25.18,62.96,1020.04,59.08,444.37], [5.11,39.4,1012.16,92.14,488.56])

testSet.take(3)

res27: Array[org.apache.spark.sql.Row] = Array([1.81,39.42,1026.92,76.97,490.55], [3.2,41.31,997.67,98.84,489.86], [3.38,41.31,998.79,97.76,489.11])

trainingSet.take(3)

res28: Array[org.apache.spark.sql.Row] = Array([2.34,39.42,1028.47,69.68,490.34], [2.58,39.42,1028.68,69.03,488.69], [2.64,39.64,1011.02,85.24,481.29])

// ***** LINEAR REGRESSION MODEL ****

import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline

// Let's initialize our linear regression learner
val lr = new LinearRegression()

import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline
lr: org.apache.spark.ml.regression.LinearRegression = linReg_955431dccb4f

frameIt: (u: String, h: Int)String

frameIt: (u: String, h: Int)String

// We use explain params to dump the parameters we can use
lr.explainParams()

res29: String =
aggregationDepth: suggested depth for treeAggregate (>= 2) (default: 2)
elasticNetParam: the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty (default: 0.0)
featuresCol: features column name (default: features)
fitIntercept: whether to fit an intercept term (default: true)
labelCol: label column name (default: label)
maxIter: maximum number of iterations (>= 0) (default: 100)
predictionCol: prediction column name (default: prediction)
regParam: regularization parameter (>= 0) (default: 0.0)
solver: the solver algorithm for optimization. If this is not set or empty, default value is 'auto' (default: auto)
standardization: whether to standardize the training features before fitting the model (default: true)
tol: the convergence tolerance for iterative algorithms (>= 0) (default: 1.0E-6)
weightCol: weight column name. If this is not set or empty, we treat all instance weights as 1.0 (undefined)

The cell below is based on the Spark ML pipeline API. More information can be found in the Spark ML Programming Guide at https://spark.apache.org/docs/latest/ml-guide.html

// Now we set the parameters for the method
lr.setPredictionCol("Predicted_PE")
  .setLabelCol("PE")
  .setMaxIter(100)
  .setRegParam(0.1)
// We will use the new spark.ml pipeline API. If you have worked with scikit-learn this will be very familiar.
val lrPipeline = new Pipeline()
lrPipeline.setStages(Array(vectorizer, lr))
// Let's first train on the entire dataset to see what we get
val lrModel = lrPipeline.fit(trainingSet)

lrPipeline: org.apache.spark.ml.Pipeline = pipeline_a16f729772ca
lrModel: org.apache.spark.ml.PipelineModel = pipeline_a16f729772ca

Since Linear Regression is simply a line of best fit over the data that minimizes the square of the error, given multiple input dimensions we can express each predictor as a line function of the form:

$y = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 + \ldots + b_i x_i + \ldots + b_k x_k$

where $b_0$ is the intercept and $b_i$'s are coefficients.

To express the coefficients of that line we can retrieve the Estimator stage from the fitted, linear-regression pipeline model named lrModel and express the weights and the intercept for the function.

// The intercept is as follows:
val intercept = lrModel.stages(1).asInstanceOf[LinearRegressionModel].intercept

intercept: Double = 427.9139822165837

// The coefficents (i.e. weights) are as follows:

val weights = lrModel.stages(1).asInstanceOf[LinearRegressionModel].coefficients.toArray

weights: Array[Double] = Array(-1.9083064919040942, -0.25381293007161654, 0.08739350304730673, -0.1474651301033126)

The model has been fit and the intercept and coefficients displayed above.

Now, let us do some work to make a string of the model that is easy to understand for an applied data scientist or data analyst.

val featuresNoLabel = dataset.columns.filter(col => col != "PE")

featuresNoLabel: Array[String] = Array(AT, V, AP, RH)

val coefficentFeaturePairs = sc.parallelize(weights).zip(sc.parallelize(featuresNoLabel))

coefficentFeaturePairs: org.apache.spark.rdd.RDD[(Double, String)] = ZippedPartitionsRDD2[108] at zip at <console>:42

coefficentFeaturePairs.collect() // this just pairs each coefficient with the name of its corresponding feature

res30: Array[(Double, String)] = Array((-1.9083064919040942,AT), (-0.25381293007161654,V), (0.08739350304730673,AP), (-0.1474651301033126,RH))

// Now let's sort the coefficients from the largest to the smallest

var equation = s"y = $intercept "
//var variables = Array
coefficentFeaturePairs.sortByKey().collect().foreach({
  case (weight, feature) =>
  { 
        val symbol = if (weight > 0) "+" else "-"
        val absWeight = Math.abs(weight)
        equation += (s" $symbol (${absWeight} * ${feature})")
  }
}
)

equation: String = y = 427.9139822165837  - (1.9083064919040942 * AT) - (0.25381293007161654 * V) - (0.1474651301033126 * RH) + (0.08739350304730673 * AP)

// Finally here is our equation
println("Linear Regression Equation: " + equation)

Linear Regression Equation: y = 427.9139822165837  - (1.9083064919040942 * AT) - (0.25381293007161654 * V) - (0.1474651301033126 * RH) + (0.08739350304730673 * AP)

Based on examining the fitted Linear Regression Equation above:

• There is a strong negative correlation between Atmospheric Temperature (AT) and Power Output due to the coefficient being greater than -1.91.
• But our other dimenensions seem to have little to no correlation with Power Output.

Do you remember Step 2: Explore Your Data? When we visualized each predictor against Power Output using a Scatter Plot, only the temperature variable seemed to have a linear correlation with Power Output so our final equation seems logical.

Now let's see what our predictions look like given this model.

val predictionsAndLabels = lrModel.transform(testSet)

display(predictionsAndLabels.select("AT", "V", "AP", "RH", "PE", "Predicted_PE"))

Truncated to 30 rows

Now that we have real predictions we can use an evaluation metric such as Root Mean Squared Error to validate our regression model. The lower the Root Mean Squared Error, the better our model.

//Now let's compute some evaluation metrics against our test dataset

import org.apache.spark.mllib.evaluation.RegressionMetrics 

val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))

import org.apache.spark.mllib.evaluation.RegressionMetrics
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@78aa5b8c

val rmse = metrics.rootMeanSquaredError

rmse: Double = 4.609375859170583

val explainedVariance = metrics.explainedVariance

explainedVariance: Double = 274.54186073318266

val r2 = metrics.r2

r2: Double = 0.9308377700269259

println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")

Root Mean Squared Error: 4.609375859170583
Explained Variance: 274.54186073318266
R2: 0.9308377700269259

Generally a good model will have 68% of predictions within 1 RMSE and 95% within 2 RMSE of the actual value. Let's calculate and see if our RMSE meets this criteria.

display(predictionsAndLabels) // recall the DataFrame predictionsAndLabels

// First we calculate the residual error and divide it by the RMSE from predictionsAndLabels DataFrame and make another DataFrame that is registered as a temporary table Power_Plant_RMSE_Evaluation
predictionsAndLabels.selectExpr("PE", "Predicted_PE", "PE - Predicted_PE AS Residual_Error", s""" (PE - Predicted_PE) / $rmse AS Within_RSME""").createOrReplaceTempView("Power_Plant_RMSE_Evaluation")

SELECT * from Power_Plant_RMSE_Evaluation

Truncated to 30 rows

-- Now we can display the RMSE as a Histogram. Clearly this shows that the RMSE is centered around 0 with the vast majority of the error within 2 RMSEs.
SELECT Within_RSME  from Power_Plant_RMSE_Evaluation

Truncated to 30 rows

We can see this definitively if we count the number of predictions within + or - 1.0 and + or - 2.0 and display this as a pie chart:

SELECT case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end RSME_Multiple, COUNT(*) count  from Power_Plant_RMSE_Evaluation
group by case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end

So we have about 70% of our training data within 1 RMSE and about 97% (70% + 27%) within 2 RMSE. So the model is pretty decent. Let's see if we can tune the model to improve it further.

NOTE: these numbers will vary across runs due to the seed in random sampling of training and test set, number of iterations, and other stopping rules in optimization, for example.

Step 7: Tuning and Evaluation

Now that we have a model with all of the data let's try to make a better model by tuning over several parameters.

import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._

import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._

First let's use a cross validator to split the data into training and validation subsets. See http://spark.apache.org/docs/latest/ml-tuning.html.

//Let's set up our evaluator class to judge the model based on the best root mean squared error
val regEval = new RegressionEvaluator()
regEval.setLabelCol("PE")
  .setPredictionCol("Predicted_PE")
  .setMetricName("rmse")

regEval: org.apache.spark.ml.evaluation.RegressionEvaluator = regEval_e2be8a782fd8
res37: regEval.type = regEval_e2be8a782fd8

We now treat the lrPipeline as an Estimator, wrapping it in a CrossValidator instance.

This will allow us to jointly choose parameters for all Pipeline stages.

A CrossValidator requires an Estimator, an Evaluator (which we set next).

//Let's create our crossvalidator with 3 fold cross validation
val crossval = new CrossValidator()
crossval.setEstimator(lrPipeline)
crossval.setNumFolds(3)
crossval.setEvaluator(regEval)

crossval: org.apache.spark.ml.tuning.CrossValidator = cv_414cd3231d9a
res38: crossval.type = cv_414cd3231d9a

A CrossValidator also requires a set of EstimatorParamMaps which we set next.

For this we need a regularization parameter (more generally a hyper-parameter that is model-specific).

Now, let's tune over our regularization parameter from 0.01 to 0.10.

val regParam = ((1 to 10) toArray).map(x => (x /100.0))

warning: there was one feature warning; re-run with -feature for details
regParam: Array[Double] = Array(0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1)

Check out the scala docs for syntactic details on org.apache.spark.ml.tuning.ParamGridBuilder.

val paramGrid = new ParamGridBuilder()
                    .addGrid(lr.regParam, regParam)
                    .build()
crossval.setEstimatorParamMaps(paramGrid)

paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
    linReg_955431dccb4f-regParam: 0.01
}, {
    linReg_955431dccb4f-regParam: 0.02
}, {
    linReg_955431dccb4f-regParam: 0.03
}, {
    linReg_955431dccb4f-regParam: 0.04
}, {
    linReg_955431dccb4f-regParam: 0.05
}, {
    linReg_955431dccb4f-regParam: 0.06
}, {
    linReg_955431dccb4f-regParam: 0.07
}, {
    linReg_955431dccb4f-regParam: 0.08
}, {
    linReg_955431dccb4f-regParam: 0.09
}, {
    linReg_955431dccb4f-regParam: 0.1
})
res39: crossval.type = cv_414cd3231d9a

//Now let's create our model
val cvModel = crossval.fit(trainingSet)

cvModel: org.apache.spark.ml.tuning.CrossValidatorModel = cv_414cd3231d9a

In addition to CrossValidator Spark also offers TrainValidationSplit for hyper-parameter tuning. TrainValidationSplit only evaluates each combination of parameters once as opposed to k times in case of CrossValidator. It is therefore less expensive, but will not produce as reliable results when the training dataset is not sufficiently large.

• http://spark.apache.org/docs/latest/ml-tuning.html#train-validation-split

Now that we have tuned let's see what we got for tuning parameters and what our RMSE was versus our intial model

val predictionsAndLabels = cvModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2

predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@2b71aef4
rmse: Double = 4.599964072968395
explainedVariance: Double = 277.2272873387723
r2: Double = 0.9311199234339246

println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")

Root Mean Squared Error: 4.599964072968395
Explained Variance: 277.2272873387723
R2: 0.9311199234339246

Let us explore other models to see if we can predict the power output better

There are several families of models in Spark's scalable machine learning library:

• http://spark.apache.org/docs/latest/ml-classification-regression.html

So our initial untuned and tuned linear regression models are statistically identical.

Given that the only linearly correlated variable is Temperature, it makes sense try another machine learning method such a Decision Tree to handle non-linear data and see if we can improve our model

A Decision Tree creates a model based on splitting variables using a tree structure. We will first start with a single decision tree model.

Reference Decision Trees: https://en.wikipedia.org/wiki/Decision*tree*learning

//Let's build a decision tree pipeline
import org.apache.spark.ml.regression.DecisionTreeRegressor

// we are using a Decision Tree Regressor as opposed to a classifier we used for the hand-written digit classification problem
val dt = new DecisionTreeRegressor()
dt.setLabelCol("PE")
dt.setPredictionCol("Predicted_PE")
dt.setFeaturesCol("features")
dt.setMaxBins(100)

val dtPipeline = new Pipeline()
dtPipeline.setStages(Array(vectorizer, dt))

import org.apache.spark.ml.regression.DecisionTreeRegressor
dt: org.apache.spark.ml.regression.DecisionTreeRegressor = dtr_23e04c8c3476
dtPipeline: org.apache.spark.ml.Pipeline = pipeline_382103e9e31e
res41: dtPipeline.type = pipeline_382103e9e31e

//Let's just resuse our CrossValidator
crossval.setEstimator(dtPipeline)

res42: crossval.type = cv_414cd3231d9a

val paramGrid = new ParamGridBuilder()
                     .addGrid(dt.maxDepth, Array(2, 3))
                     .build()

paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
    dtr_23e04c8c3476-maxDepth: 2
}, {
    dtr_23e04c8c3476-maxDepth: 3
})

crossval.setEstimatorParamMaps(paramGrid)

res43: crossval.type = cv_414cd3231d9a

val dtModel = crossval.fit(trainingSet) // fit decitionTree with cv

dtModel: org.apache.spark.ml.tuning.CrossValidatorModel = cv_414cd3231d9a

import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel].toDebugString

import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
res44: String =
"DecisionTreeRegressionModel (uid=dtr_23e04c8c3476) of depth 3 with 15 nodes
  If (feature 0 <= 17.84)
   If (feature 0 <= 11.95)
    If (feature 0 <= 8.75)
     Predict: 483.5412151067323
    Else (feature 0 > 8.75)
     Predict: 475.6305502392345
   Else (feature 0 > 11.95)
    If (feature 0 <= 15.33)
     Predict: 467.63141917293234
    Else (feature 0 > 15.33)
     Predict: 460.74754125412574
  Else (feature 0 > 17.84)
   If (feature 0 <= 23.02)
    If (feature 1 <= 47.83)
     Predict: 457.1077966101695
    Else (feature 1 > 47.83)
     Predict: 448.74750213858016
   Else (feature 0 > 23.02)
    If (feature 1 <= 66.25)
     Predict: 442.88544855967086
    Else (feature 1 > 66.25)
     Predict: 434.7293710691822
"

The line above will pull the Decision Tree model from the Pipeline and display it as an if-then-else string.

Next let's visualize it as a decision tree for regression.

display(dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel])

Now let's see how our DecisionTree model compares to our LinearRegression model

val predictionsAndLabels = dtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2

println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")

Root Mean Squared Error: 5.221342219456633
Explained Variance: 269.66550072645475
R2: 0.9112539444165726
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@1b14107a
rmse: Double = 5.221342219456633
explainedVariance: Double = 269.66550072645475
r2: Double = 0.9112539444165726

So our DecisionTree was slightly worse than our LinearRegression model (LR: 4.6 vs DT: 5.2). Maybe we can try an Ensemble method such as Gradient-Boosted Decision Trees to see if we can strengthen our model by using an ensemble of weaker trees with weighting to reduce the error in our model.

Note since this is a complex model, the cell below can take about 16 minutes* or so to run on a small cluster with a couple nodes with about 6GB RAM, go out and grab a coffee and come back :-).*

This GBTRegressor code will be way faster on a larger cluster of course.

A visual explanation of gradient boosted trees:

• http://arogozhnikov.github.io/2016/06/24/gradientboostingexplained.html

Let's see what a boosting algorithm, a type of ensemble method, is all about in more detail.

This can take between 5 - 15 minutes in a shard with 6 workers depending on other workloads (may be longer in the Community Edition).

import org.apache.spark.ml.regression.GBTRegressor

val gbt = new GBTRegressor()
gbt.setLabelCol("PE")
gbt.setPredictionCol("Predicted_PE")
gbt.setFeaturesCol("features")
gbt.setSeed(100088121L)
gbt.setMaxBins(100)
gbt.setMaxIter(120)

val gbtPipeline = new Pipeline()
gbtPipeline.setStages(Array(vectorizer, gbt))
//Let's just resuse our CrossValidator

crossval.setEstimator(gbtPipeline)

val paramGrid = new ParamGridBuilder()
  .addGrid(gbt.maxDepth, Array(2, 3))
  .build()
crossval.setEstimatorParamMaps(paramGrid)

//gbt.explainParams
val gbtModel = crossval.fit(trainingSet)

import org.apache.spark.ml.regression.GBTRegressor
gbt: org.apache.spark.ml.regression.GBTRegressor = gbtr_9c5ab45fe584
gbtPipeline: org.apache.spark.ml.Pipeline = pipeline_e6a84d2d75ba
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
    gbtr_9c5ab45fe584-maxDepth: 2
}, {
    gbtr_9c5ab45fe584-maxDepth: 3
})
gbtModel: org.apache.spark.ml.tuning.CrossValidatorModel = cv_414cd3231d9a

import org.apache.spark.ml.regression.GBTRegressionModel 

val predictionsAndLabels = gbtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2


println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")

Root Mean Squared Error: 3.7616562931536803
Explained Variance: 282.4365553123402
R2: 0.9539379816689415
import org.apache.spark.ml.regression.GBTRegressionModel
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@1f1d9c34
rmse: Double = 3.7616562931536803
explainedVariance: Double = 282.4365553123402
r2: Double = 0.9539379816689415

Note that the root mean squared error is smaller now due to the ensemble of 120 trees from Gradient Boosting!

We can use the toDebugString method to dump out what our trees and weighting look like:

gbtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[GBTRegressionModel].toDebugString

res49: String =
"GBTRegressionModel (uid=gbtr_9c5ab45fe584) with 120 trees
  Tree 0 (weight 1.0):
    If (feature 0 <= 17.84)
     If (feature 0 <= 11.95)
      If (feature 0 <= 8.75)
       Predict: 483.5412151067323
      Else (feature 0 > 8.75)
       Predict: 475.6305502392345
     Else (feature 0 > 11.95)
      If (feature 0 <= 15.33)
       Predict: 467.63141917293234
      Else (feature 0 > 15.33)
       Predict: 460.74754125412574
    Else (feature 0 > 17.84)
     If (feature 0 <= 23.02)
      If (feature 1 <= 47.83)
       Predict: 457.1077966101695
      Else (feature 1 > 47.83)
       Predict: 448.74750213858016
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: 442.88544855967086
      Else (feature 1 > 66.25)
       Predict: 434.7293710691822
  Tree 1 (weight 0.1):
    If (feature 2 <= 1009.9)
     If (feature 1 <= 43.13)
      If (feature 0 <= 15.33)
       Predict: -0.31094207231231485
      Else (feature 0 > 15.33)
       Predict: 4.302958436537365
     Else (feature 1 > 43.13)
      If (feature 0 <= 23.02)
       Predict: -8.38392506141353
      Else (feature 0 > 23.02)
       Predict: -2.399960976520273
    Else (feature 2 > 1009.9)
     If (feature 3 <= 86.21)
      If (feature 0 <= 26.35)
       Predict: 2.888623754019027
      Else (feature 0 > 26.35)
       Predict: -1.1489483044194229
     Else (feature 3 > 86.21)
      If (feature 1 <= 39.72)
       Predict: 3.876324424163314
      Else (feature 1 > 39.72)
       Predict: -3.058952828112949
  Tree 2 (weight 0.1):
    If (feature 2 <= 1009.63)
     If (feature 1 <= 43.13)
      If (feature 0 <= 11.95)
       Predict: -1.4091086031845625
      Else (feature 0 > 11.95)
       Predict: 2.6329466235800942
     Else (feature 1 > 43.13)
      If (feature 0 <= 23.02)
       Predict: -6.795414480322956
      Else (feature 0 > 23.02)
       Predict: -2.166560698742912
    Else (feature 2 > 1009.63)
     If (feature 3 <= 80.44)
      If (feature 0 <= 26.98)
       Predict: 2.878622882275939
      Else (feature 0 > 26.98)
       Predict: -1.146426969990865
     Else (feature 3 > 80.44)
      If (feature 3 <= 94.55)
       Predict: -0.35885921725905906
      Else (feature 3 > 94.55)
       Predict: -5.75364586186002
  Tree 3 (weight 0.1):
    If (feature 0 <= 27.6)
     If (feature 3 <= 70.2)
      If (feature 1 <= 40.05)
       Predict: -0.9480831286616939
      Else (feature 1 > 40.05)
       Predict: 3.660397090904016
     Else (feature 3 > 70.2)
      If (feature 1 <= 40.64)
       Predict: 2.1539405832035627
      Else (feature 1 > 40.64)
       Predict: -1.2281619807661366
    Else (feature 0 > 27.6)
     If (feature 1 <= 65.27)
      If (feature 2 <= 1005.99)
       Predict: -15.33433697033558
      Else (feature 2 > 1005.99)
       Predict: -5.866095468145647
     Else (feature 1 > 65.27)
      If (feature 2 <= 1008.75)
       Predict: -4.03431044067007
      Else (feature 2 > 1008.75)
       Predict: -0.23440867445577207
  Tree 4 (weight 0.1):
    If (feature 0 <= 26.35)
     If (feature 0 <= 23.02)
      If (feature 1 <= 68.67)
       Predict: 0.12035773384797814
      Else (feature 1 > 68.67)
       Predict: -13.928523073642005
     Else (feature 0 > 23.02)
      If (feature 0 <= 24.57)
       Predict: 5.5622340839882165
      Else (feature 0 > 24.57)
       Predict: 1.6938172370244715
    Else (feature 0 > 26.35)
     If (feature 1 <= 66.25)
      If (feature 2 <= 1008.4)
       Predict: -9.009916879825393
      Else (feature 2 > 1008.4)
       Predict: -3.059736394918022
     Else (feature 1 > 66.25)
      If (feature 0 <= 30.2)
       Predict: 0.14704705100738577
      Else (feature 0 > 30.2)
       Predict: -3.2914123948921006
  Tree 5 (weight 0.1):
    If (feature 2 <= 1010.41)
     If (feature 1 <= 43.41)
      If (feature 3 <= 99.27)
       Predict: 1.2994444710077233
      Else (feature 3 > 99.27)
       Predict: -6.649548317319231
     Else (feature 1 > 43.41)
      If (feature 0 <= 23.02)
       Predict: -4.9119452777748
      Else (feature 0 > 23.02)
       Predict: -0.9514185089440673
    Else (feature 2 > 1010.41)
     If (feature 3 <= 89.83)
      If (feature 0 <= 31.26)
       Predict: 1.2914123584761403
      Else (feature 0 > 31.26)
       Predict: -5.115001417285994
     Else (feature 3 > 89.83)
      If (feature 1 <= 40.64)
       Predict: 1.5160976219176363
      Else (feature 1 > 40.64)
       Predict: -4.202813699523934
  Tree 6 (weight 0.1):
    If (feature 2 <= 1007.27)
     If (feature 0 <= 27.94)
      If (feature 3 <= 71.09)
       Predict: 1.616448005210527
      Else (feature 3 > 71.09)
       Predict: -2.1313527108274157
     Else (feature 0 > 27.94)
      If (feature 1 <= 68.3)
       Predict: -8.579840063013142
      Else (feature 1 > 68.3)
       Predict: -1.915909819494233
    Else (feature 2 > 1007.27)
     If (feature 3 <= 95.45)
      If (feature 0 <= 6.52)
       Predict: 4.973465595410054
      Else (feature 0 > 6.52)
       Predict: 0.3837975458985242
     Else (feature 3 > 95.45)
      If (feature 2 <= 1013.43)
       Predict: -0.8175453481344352
      Else (feature 2 > 1013.43)
       Predict: -7.264843604639278
  Tree 7 (weight 0.1):
    If (feature 0 <= 26.35)
     If (feature 3 <= 71.09)
      If (feature 1 <= 67.83)
       Predict: 1.9620965187817083
      Else (feature 1 > 67.83)
       Predict: 7.953863660960779
     Else (feature 3 > 71.09)
      If (feature 1 <= 40.89)
       Predict: 1.2020440154192213
      Else (feature 1 > 40.89)
       Predict: -0.9989659748111419
    Else (feature 0 > 26.35)
     If (feature 1 <= 66.25)
      If (feature 2 <= 1008.4)
       Predict: -6.230272922553423
      Else (feature 2 > 1008.4)
       Predict: -2.654681371247991
     Else (feature 1 > 66.25)
      If (feature 2 <= 1004.52)
       Predict: -3.9527797601131853
      Else (feature 2 > 1004.52)
       Predict: -0.21770148036273387
  Tree 8 (weight 0.1):
    If (feature 0 <= 29.56)
     If (feature 3 <= 63.16)
      If (feature 1 <= 72.24)
       Predict: 1.9612116105231265
      Else (feature 1 > 72.24)
       Predict: 8.756949826030025
     Else (feature 3 > 63.16)
      If (feature 0 <= 5.95)
       Predict: 4.445363585074405
      Else (feature 0 > 5.95)
       Predict: -0.4097996897633835
    Else (feature 0 > 29.56)
     If (feature 1 <= 68.3)
      If (feature 2 <= 1009.9)
       Predict: -7.882200867406393
      Else (feature 2 > 1009.9)
       Predict: -1.7273221348184091
     Else (feature 1 > 68.3)
      If (feature 2 <= 1013.77)
       Predict: -0.7219749804525829
      Else (feature 2 > 1013.77)
       Predict: -6.492100849806538
  Tree 9 (weight 0.1):
    If (feature 3 <= 89.83)
     If (feature 0 <= 25.72)
      If (feature 0 <= 23.02)
       Predict: 0.15450088997272685
      Else (feature 0 > 23.02)
       Predict: 3.010254802875794
     Else (feature 0 > 25.72)
      If (feature 1 <= 66.25)
       Predict: -2.5821765284417615
      Else (feature 1 > 66.25)
       Predict: -0.3935112713804148
    Else (feature 3 > 89.83)
     If (feature 2 <= 1019.52)
      If (feature 0 <= 7.08)
       Predict: 3.264389020443774
      Else (feature 0 > 7.08)
       Predict: -1.6246048211383168
     Else (feature 2 > 1019.52)
      If (feature 0 <= 8.75)
       Predict: -8.005340799169343
      Else (feature 0 > 8.75)
       Predict: -2.9832409167030063
  Tree 10 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 0 <= 17.84)
      If (feature 1 <= 45.87)
       Predict: 0.26309432916452813
      Else (feature 1 > 45.87)
       Predict: -5.716473785544373
     Else (feature 0 > 17.84)
      If (feature 2 <= 1012.56)
       Predict: -0.15863259341493433
      Else (feature 2 > 1012.56)
       Predict: 7.899625065937478
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 3 <= 67.72)
       Predict: -27.101084325134025
      Else (feature 3 > 67.72)
       Predict: -12.755339130015875
     Else (feature 0 > 17.84)
      If (feature 0 <= 20.6)
       Predict: 3.8741798886113408
      Else (feature 0 > 20.6)
       Predict: -0.8179571837367839
  Tree 11 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 74.22)
      If (feature 1 <= 59.14)
       Predict: -0.6678644068375302
      Else (feature 1 > 59.14)
       Predict: -5.0251736913870495
     Else (feature 1 > 74.22)
      If (feature 2 <= 1000.68)
       Predict: -1.9453153753750236
      Else (feature 2 > 1000.68)
       Predict: 3.954565899065237
    Else (feature 2 > 1004.52)
     If (feature 3 <= 60.81)
      If (feature 0 <= 29.27)
       Predict: 2.256991118214201
      Else (feature 0 > 29.27)
       Predict: -0.8956432652281918
     Else (feature 3 > 60.81)
      If (feature 0 <= 5.18)
       Predict: 5.30208686561611
      Else (feature 0 > 5.18)
       Predict: -0.2275806642044292
  Tree 12 (weight 0.1):
    If (feature 3 <= 93.63)
     If (feature 0 <= 20.6)
      If (feature 0 <= 17.84)
       Predict: -0.13650451477274114
      Else (feature 0 > 17.84)
       Predict: 4.26138638419226
     Else (feature 0 > 20.6)
      If (feature 0 <= 23.02)
       Predict: -4.145788149131118
      Else (feature 0 > 23.02)
       Predict: 0.45010060784860767
    Else (feature 3 > 93.63)
     If (feature 0 <= 11.95)
      If (feature 0 <= 6.52)
       Predict: 1.9630864105825856
      Else (feature 0 > 6.52)
       Predict: -5.847103580294793
     Else (feature 0 > 11.95)
      If (feature 1 <= 57.85)
       Predict: 1.6850763767018282
      Else (feature 1 > 57.85)
       Predict: -3.57522814358917
  Tree 13 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.39)
      If (feature 0 <= 13.56)
       Predict: 0.7497248523199469
      Else (feature 0 > 13.56)
       Predict: -0.8096048572768345
     Else (feature 1 > 49.39)
      If (feature 0 <= 17.84)
       Predict: -4.9975868045736025
      Else (feature 0 > 17.84)
       Predict: 6.70181838603398
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 1 <= 58.62)
       Predict: -8.139327595464518
      Else (feature 1 > 58.62)
       Predict: -11.260696586956563
     Else (feature 0 > 17.84)
      If (feature 2 <= 1020.32)
       Predict: -0.4173502593107514
      Else (feature 2 > 1020.32)
       Predict: 7.350524302545053
  Tree 14 (weight 0.1):
    If (feature 2 <= 1009.3)
     If (feature 1 <= 73.67)
      If (feature 0 <= 26.35)
       Predict: -0.2834715308768144
      Else (feature 0 > 26.35)
       Predict: -2.2855655986052446
     Else (feature 1 > 73.67)
      If (feature 0 <= 21.42)
       Predict: -19.886551554013977
      Else (feature 0 > 21.42)
       Predict: 1.8345107899392203
    Else (feature 2 > 1009.3)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.2012146645141011
      Else (feature 1 > 46.93)
       Predict: -5.331252849501989
     Else (feature 0 > 17.84)
      If (feature 0 <= 20.6)
       Predict: 3.9009310043506518
      Else (feature 0 > 20.6)
       Predict: 0.05492627340134294
  Tree 15 (weight 0.1):
    If (feature 3 <= 80.44)
     If (feature 0 <= 26.57)
      If (feature 0 <= 23.02)
       Predict: 0.24935555983937532
      Else (feature 0 > 23.02)
       Predict: 1.9734839371689987
     Else (feature 0 > 26.57)
      If (feature 1 <= 66.25)
       Predict: -2.652691255012269
      Else (feature 1 > 66.25)
       Predict: 0.10205623249441657
    Else (feature 3 > 80.44)
     If (feature 1 <= 57.85)
      If (feature 2 <= 1021.65)
       Predict: 0.3189331596273633
      Else (feature 2 > 1021.65)
       Predict: -2.493847422724499
     Else (feature 1 > 57.85)
      If (feature 0 <= 23.02)
       Predict: -4.443277995263894
      Else (feature 0 > 23.02)
       Predict: 1.0414575062489446
  Tree 16 (weight 0.1):
    If (feature 0 <= 6.52)
     If (feature 3 <= 67.72)
      If (feature 1 <= 39.48)
       Predict: -0.021931809818089017
      Else (feature 1 > 39.48)
       Predict: 17.644618798102908
     Else (feature 3 > 67.72)
      If (feature 1 <= 42.07)
       Predict: 2.6927240976688487
      Else (feature 1 > 42.07)
       Predict: -3.720328734281554
    Else (feature 0 > 6.52)
     If (feature 0 <= 8.75)
      If (feature 0 <= 7.97)
       Predict: -1.1870026837027776
      Else (feature 0 > 7.97)
       Predict: -6.311604790035118
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.73)
       Predict: 5.036277690956247
      Else (feature 0 > 9.73)
       Predict: -0.07156864179175153
  Tree 17 (weight 0.1):
    If (feature 2 <= 1005.35)
     If (feature 1 <= 70.8)
      If (feature 0 <= 21.14)
       Predict: 0.2557898848412102
      Else (feature 0 > 21.14)
       Predict: -4.092246463553751
     Else (feature 1 > 70.8)
      If (feature 0 <= 23.02)
       Predict: -17.7762740471523
      Else (feature 0 > 23.02)
       Predict: 1.4679036019616782
    Else (feature 2 > 1005.35)
     If (feature 3 <= 60.81)
      If (feature 2 <= 1021.17)
       Predict: 0.8109918761137652
      Else (feature 2 > 1021.17)
       Predict: 6.491756407811347
     Else (feature 3 > 60.81)
      If (feature 0 <= 25.72)
       Predict: 0.06495066055048145
      Else (feature 0 > 25.72)
       Predict: -1.234843690619109
  Tree 18 (weight 0.1):
    If (feature 3 <= 93.63)
     If (feature 0 <= 13.56)
      If (feature 0 <= 11.95)
       Predict: -0.1389635939018028
      Else (feature 0 > 11.95)
       Predict: 4.085304226900187
     Else (feature 0 > 13.56)
      If (feature 0 <= 15.33)
       Predict: -3.558076811842663
      Else (feature 0 > 15.33)
       Predict: 0.24840255719067195
    Else (feature 3 > 93.63)
     If (feature 0 <= 11.95)
      If (feature 0 <= 6.52)
       Predict: 1.1725211739721944
      Else (feature 0 > 6.52)
       Predict: -4.696815201291802
     Else (feature 0 > 11.95)
      If (feature 0 <= 23.42)
       Predict: -0.1435586215485262
      Else (feature 0 > 23.42)
       Predict: 6.017267110381734
  Tree 19 (weight 0.1):
    If (feature 0 <= 29.89)
     If (feature 3 <= 46.38)
      If (feature 2 <= 1020.32)
       Predict: 2.734528637686715
      Else (feature 2 > 1020.32)
       Predict: 14.229272221061546
     Else (feature 3 > 46.38)
      If (feature 1 <= 73.18)
       Predict: -0.09112932077559661
      Else (feature 1 > 73.18)
       Predict: 2.171636618202333
    Else (feature 0 > 29.89)
     If (feature 1 <= 68.3)
      If (feature 2 <= 1012.96)
       Predict: -4.842672386234583
      Else (feature 2 > 1012.96)
       Predict: 0.4656753436410731
     Else (feature 1 > 68.3)
      If (feature 1 <= 69.88)
       Predict: 1.9998755414672877
      Else (feature 1 > 69.88)
       Predict: -1.377187598546301
  Tree 20 (weight 0.1):
    If (feature 1 <= 40.89)
     If (feature 0 <= 11.95)
      If (feature 0 <= 10.74)
       Predict: 0.3474341793041741
      Else (feature 0 > 10.74)
       Predict: -3.2174625433704844
     Else (feature 0 > 11.95)
      If (feature 0 <= 13.56)
       Predict: 6.2521753652461385
      Else (feature 0 > 13.56)
       Predict: 0.7467107076401086
    Else (feature 1 > 40.89)
     If (feature 1 <= 41.16)
      If (feature 2 <= 1011.9)
       Predict: 1.6159428806525291
      Else (feature 2 > 1011.9)
       Predict: -5.525791920129847
     Else (feature 1 > 41.16)
      If (feature 1 <= 41.48)
       Predict: 2.3655609293253264
      Else (feature 1 > 41.48)
       Predict: -0.18730957785387015
  Tree 21 (weight 0.1):
    If (feature 0 <= 7.08)
     If (feature 1 <= 41.58)
      If (feature 1 <= 41.16)
       Predict: 1.9153935195932974
      Else (feature 1 > 41.16)
       Predict: 7.0746807427814735
     Else (feature 1 > 41.58)
      If (feature 2 <= 1020.77)
       Predict: -1.256554177586309
      Else (feature 2 > 1020.77)
       Predict: -26.29941855196938
    Else (feature 0 > 7.08)
     If (feature 0 <= 8.75)
      If (feature 1 <= 37.8)
       Predict: -8.544132394601597
      Else (feature 1 > 37.8)
       Predict: -2.6184141709801976
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.73)
       Predict: 4.069411815161333
      Else (feature 0 > 9.73)
       Predict: -0.06494039395966968
  Tree 22 (weight 0.1):
    If (feature 0 <= 23.02)
     If (feature 0 <= 21.69)
      If (feature 0 <= 15.33)
       Predict: -0.48298234147973435
      Else (feature 0 > 15.33)
       Predict: 1.2747845905419344
     Else (feature 0 > 21.69)
      If (feature 1 <= 66.25)
       Predict: -3.44223180465188
      Else (feature 1 > 66.25)
       Predict: -9.677838572965495
    Else (feature 0 > 23.02)
     If (feature 0 <= 24.39)
      If (feature 1 <= 66.25)
       Predict: 1.4289485230939327
      Else (feature 1 > 66.25)
       Predict: 7.493228657621072
     Else (feature 0 > 24.39)
      If (feature 1 <= 66.25)
       Predict: -1.55164310941819
      Else (feature 1 > 66.25)
       Predict: 0.5159038364280375
  Tree 23 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 66.93)
      If (feature 1 <= 43.41)
       Predict: 0.8366856528539243
      Else (feature 1 > 43.41)
       Predict: -2.146264827541657
     Else (feature 1 > 66.93)
      If (feature 0 <= 23.02)
       Predict: -4.593173040738928
      Else (feature 0 > 23.02)
       Predict: 0.7595925761507126
    Else (feature 2 > 1010.89)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.38)
       Predict: 0.19019050526253845
      Else (feature 0 > 14.38)
       Predict: -4.931089744789576
     Else (feature 0 > 15.33)
      If (feature 1 <= 56.57)
       Predict: 2.893896440054576
      Else (feature 1 > 56.57)
       Predict: -0.2411893147021192
  Tree 24 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 39.13)
      If (feature 0 <= 16.56)
       Predict: 5.674347262101248
      Else (feature 0 > 16.56)
       Predict: -15.35003850200303
     Else (feature 1 > 39.13)
      If (feature 1 <= 70.8)
       Predict: -2.2136597249782484
      Else (feature 1 > 70.8)
       Predict: 0.4854909471410394
    Else (feature 2 > 1004.52)
     If (feature 0 <= 23.02)
      If (feature 0 <= 21.14)
       Predict: 0.25072963079321764
      Else (feature 0 > 21.14)
       Predict: -3.1127381475029745
     Else (feature 0 > 23.02)
      If (feature 0 <= 24.98)
       Predict: 2.513302584995404
      Else (feature 0 > 24.98)
       Predict: -0.17126775916442186
  Tree 25 (weight 0.1):
    If (feature 3 <= 76.79)
     If (feature 0 <= 28.75)
      If (feature 1 <= 66.25)
       Predict: 0.1271610430935476
      Else (feature 1 > 66.25)
       Predict: 2.4600009065275934
     Else (feature 0 > 28.75)
      If (feature 1 <= 44.58)
       Predict: -10.925990145829292
      Else (feature 1 > 44.58)
       Predict: -0.7031644656131009
    Else (feature 3 > 76.79)
     If (feature 0 <= 20.9)
      If (feature 0 <= 17.84)
       Predict: -0.3807566877980857
      Else (feature 0 > 17.84)
       Predict: 2.329590528017136
     Else (feature 0 > 20.9)
      If (feature 0 <= 23.02)
       Predict: -3.741947089345415
      Else (feature 0 > 23.02)
       Predict: -0.3619479813878585
  Tree 26 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 42.07)
      If (feature 3 <= 84.36)
       Predict: 5.869887042156764
      Else (feature 3 > 84.36)
       Predict: 2.3621425360574837
     Else (feature 1 > 42.07)
      If (feature 2 <= 1007.82)
       Predict: -1.4185266335795177
      Else (feature 2 > 1007.82)
       Predict: -5.383717178467172
    Else (feature 0 > 5.18)
     If (feature 3 <= 53.32)
      If (feature 2 <= 1021.17)
       Predict: 0.6349729680247564
      Else (feature 2 > 1021.17)
       Predict: 9.504309080910616
     Else (feature 3 > 53.32)
      If (feature 0 <= 25.95)
       Predict: 0.010243524812335326
      Else (feature 0 > 25.95)
       Predict: -0.8173343910336555
  Tree 27 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 1 <= 74.87)
      If (feature 1 <= 56.57)
       Predict: 0.28085003688072396
      Else (feature 1 > 56.57)
       Predict: -0.378551674966564
     Else (feature 1 > 74.87)
      If (feature 0 <= 21.42)
       Predict: -12.321588273833015
      Else (feature 0 > 21.42)
       Predict: 1.8659669412137414
    Else (feature 2 > 1028.38)
     If (feature 3 <= 89.83)
      If (feature 3 <= 66.27)
       Predict: -8.252928408643971
      Else (feature 3 > 66.27)
       Predict: -2.023910717088332
     Else (feature 3 > 89.83)
      If (feature 0 <= 8.39)
       Predict: -11.472893448110653
      Else (feature 0 > 8.39)
       Predict: -8.030312146910243
  Tree 28 (weight 0.1):
    If (feature 3 <= 85.4)
     If (feature 0 <= 7.55)
      If (feature 1 <= 40.05)
       Predict: 0.3456361310433187
      Else (feature 1 > 40.05)
       Predict: 4.958188742864418
     Else (feature 0 > 7.55)
      If (feature 0 <= 8.75)
       Predict: -3.0608059226719657
      Else (feature 0 > 8.75)
       Predict: 0.16507864507530287
    Else (feature 3 > 85.4)
     If (feature 2 <= 1015.63)
      If (feature 2 <= 1014.19)
       Predict: -0.3593841710339432
      Else (feature 2 > 1014.19)
       Predict: 3.2531365191458024
     Else (feature 2 > 1015.63)
      If (feature 1 <= 40.64)
       Predict: 1.0007657377910708
      Else (feature 1 > 40.64)
       Predict: -2.132339394694771
  Tree 29 (weight 0.1):
    If (feature 0 <= 30.56)
     If (feature 3 <= 55.74)
      If (feature 1 <= 72.24)
       Predict: 0.8569729911086951
      Else (feature 1 > 72.24)
       Predict: 6.358127096088517
     Else (feature 3 > 55.74)
      If (feature 1 <= 41.48)
       Predict: 0.43148253820326676
      Else (feature 1 > 41.48)
       Predict: -0.24352278568573174
    Else (feature 0 > 30.56)
     If (feature 2 <= 1014.35)
      If (feature 1 <= 68.3)
       Predict: -2.5522103291398683
      Else (feature 1 > 68.3)
       Predict: -0.21266182300917044
     Else (feature 2 > 1014.35)
      If (feature 1 <= 74.87)
       Predict: -6.498613011225412
      Else (feature 1 > 74.87)
       Predict: 0.9765776955731879
  Tree 30 (weight 0.1):
    If (feature 0 <= 17.84)
     If (feature 1 <= 45.08)
      If (feature 0 <= 15.33)
       Predict: -0.14424299831222268
      Else (feature 0 > 15.33)
       Predict: 1.8754751416891788
     Else (feature 1 > 45.08)
      If (feature 2 <= 1020.77)
       Predict: -3.097730832691005
      Else (feature 2 > 1020.77)
       Predict: -8.90070153022011
    Else (feature 0 > 17.84)
     If (feature 0 <= 18.71)
      If (feature 1 <= 49.02)
       Predict: 1.2726140970398088
      Else (feature 1 > 49.02)
       Predict: 6.649324687634596
     Else (feature 0 > 18.71)
      If (feature 1 <= 46.93)
       Predict: -2.818245204603037
      Else (feature 1 > 46.93)
       Predict: 0.23586447368304939
  Tree 31 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 59.14)
      If (feature 1 <= 50.66)
       Predict: -0.8733348655196066
      Else (feature 1 > 50.66)
       Predict: 7.928862441716025
     Else (feature 1 > 59.14)
      If (feature 1 <= 70.8)
       Predict: -3.8112988828197807
      Else (feature 1 > 70.8)
       Predict: 0.42812840935226704
    Else (feature 2 > 1004.52)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.07282772802501089
      Else (feature 1 > 46.93)
       Predict: -3.3364389464988706
     Else (feature 0 > 17.84)
      If (feature 2 <= 1020.32)
       Predict: 0.18419167853517965
      Else (feature 2 > 1020.32)
       Predict: 6.584432032190064
  Tree 32 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.39)
      If (feature 0 <= 13.56)
       Predict: 0.36741135502935035
      Else (feature 0 > 13.56)
       Predict: -0.7178818728654812
     Else (feature 1 > 49.39)
      If (feature 0 <= 17.84)
       Predict: -1.7883686826457996
      Else (feature 0 > 17.84)
       Predict: 4.519745157967235
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 0 <= 17.5)
       Predict: -4.182857837547887
      Else (feature 0 > 17.5)
       Predict: -7.917768935292194
     Else (feature 0 > 17.84)
      If (feature 0 <= 19.61)
       Predict: 2.6880627533068244
      Else (feature 0 > 19.61)
       Predict: -0.2998975340288976
  Tree 33 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 11.03)
      If (feature 3 <= 93.63)
       Predict: 0.7278554646891878
      Else (feature 3 > 93.63)
       Predict: -2.2492543009893162
     Else (feature 0 > 11.03)
      If (feature 2 <= 1024.3)
       Predict: -5.536706488618952
      Else (feature 2 > 1024.3)
       Predict: 4.479707018501001
    Else (feature 0 > 11.95)
     If (feature 0 <= 13.08)
      If (feature 0 <= 12.5)
       Predict: 5.173128471411881
      Else (feature 0 > 12.5)
       Predict: 2.3834255982190755
     Else (feature 0 > 13.08)
      If (feature 0 <= 15.33)
       Predict: -1.5022006203890645
      Else (feature 0 > 15.33)
       Predict: 0.15423852245074754
  Tree 34 (weight 0.1):
    If (feature 0 <= 8.75)
     If (feature 0 <= 7.55)
      If (feature 3 <= 77.56)
       Predict: 3.015852739381847
      Else (feature 3 > 77.56)
       Predict: -0.06103236076131486
     Else (feature 0 > 7.55)
      If (feature 3 <= 62.1)
       Predict: -13.594573386743992
      Else (feature 3 > 62.1)
       Predict: -2.6914920546129273
    Else (feature 0 > 8.75)
     If (feature 0 <= 10.03)
      If (feature 3 <= 95.45)
       Predict: 3.213047453934116
      Else (feature 3 > 95.45)
       Predict: -2.3699077010186502
     Else (feature 0 > 10.03)
      If (feature 0 <= 11.95)
       Predict: -1.841483689919706
      Else (feature 0 > 11.95)
       Predict: 0.1034719724734039
  Tree 35 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.02)
      If (feature 1 <= 44.88)
       Predict: 0.1854471597033813
      Else (feature 1 > 44.88)
       Predict: -1.537157071790549
     Else (feature 1 > 49.02)
      If (feature 2 <= 1009.77)
       Predict: -0.7176011396833722
      Else (feature 2 > 1009.77)
       Predict: 3.4414962844541495
    Else (feature 1 > 56.57)
     If (feature 1 <= 66.25)
      If (feature 0 <= 21.92)
       Predict: 0.6042503983890641
      Else (feature 0 > 21.92)
       Predict: -1.6430682984491796
     Else (feature 1 > 66.25)
      If (feature 0 <= 23.02)
       Predict: -3.919778656895867
      Else (feature 0 > 23.02)
       Predict: 0.8520833743461524
  Tree 36 (weight 0.1):
    If (feature 0 <= 27.6)
     If (feature 0 <= 23.02)
      If (feature 0 <= 22.1)
       Predict: 0.08610814822616036
      Else (feature 0 > 22.1)
       Predict: -3.39446668206219
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: -0.25067209339950686
      Else (feature 1 > 66.25)
       Predict: 2.1536703058787143
    Else (feature 0 > 27.6)
     If (feature 3 <= 62.1)
      If (feature 1 <= 74.87)
       Predict: -0.3912307208100507
      Else (feature 1 > 74.87)
       Predict: 2.6168301411252224
     Else (feature 3 > 62.1)
      If (feature 1 <= 71.8)
       Predict: -0.1075335658351684
      Else (feature 1 > 71.8)
       Predict: -3.3756176659678685
  Tree 37 (weight 0.1):
    If (feature 0 <= 25.35)
     If (feature 0 <= 23.02)
      If (feature 1 <= 64.84)
       Predict: 0.07789630965601392
      Else (feature 1 > 64.84)
       Predict: -2.8928836560033093
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: 0.13731068060749954
      Else (feature 1 > 66.25)
       Predict: 4.15851454889221
    Else (feature 0 > 25.35)
     If (feature 1 <= 43.65)
      If (feature 0 <= 27.19)
       Predict: -16.475158304770883
      Else (feature 0 > 27.19)
       Predict: -7.947134756554647
     Else (feature 1 > 43.65)
      If (feature 3 <= 62.7)
       Predict: 0.1725950049938879
      Else (feature 3 > 62.7)
       Predict: -1.0926147971432427
  Tree 38 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 0 <= 30.56)
      If (feature 3 <= 47.89)
       Predict: 1.6647926733523803
      Else (feature 3 > 47.89)
       Predict: 0.019004190066623235
     Else (feature 0 > 30.56)
      If (feature 2 <= 1014.35)
       Predict: -0.6192794789083232
      Else (feature 2 > 1014.35)
       Predict: -4.385760311827676
    Else (feature 2 > 1028.38)
     If (feature 1 <= 39.48)
      If (feature 0 <= 6.52)
       Predict: 4.573467616169609
      Else (feature 0 > 6.52)
       Predict: -1.362091279334777
     Else (feature 1 > 39.48)
      If (feature 0 <= 8.75)
       Predict: -7.0007999537928605
      Else (feature 0 > 8.75)
       Predict: -1.617908469279585
  Tree 39 (weight 0.1):
    If (feature 2 <= 1017.42)
     If (feature 2 <= 1014.19)
      If (feature 1 <= 43.13)
       Predict: 1.2098492492388833
      Else (feature 1 > 43.13)
       Predict: -0.4345828650352739
     Else (feature 2 > 1014.19)
      If (feature 3 <= 96.38)
       Predict: 1.0830640036331665
      Else (feature 3 > 96.38)
       Predict: -6.6054777318343785
    Else (feature 2 > 1017.42)
     If (feature 2 <= 1019.23)
      If (feature 1 <= 57.85)
       Predict: -0.8212874032064794
      Else (feature 1 > 57.85)
       Predict: -2.6667829000634105
     Else (feature 2 > 1019.23)
      If (feature 0 <= 17.84)
       Predict: -0.39094381687835245
      Else (feature 0 > 17.84)
       Predict: 3.336117383932137
  Tree 40 (weight 0.1):
    If (feature 3 <= 75.23)
     If (feature 1 <= 40.05)
      If (feature 1 <= 39.96)
       Predict: -1.2851367407493581
      Else (feature 1 > 39.96)
       Predict: -9.117459296991676
     Else (feature 1 > 40.05)
      If (feature 1 <= 40.89)
       Predict: 4.461974679211411
      Else (feature 1 > 40.89)
       Predict: 0.25422282080546216
    Else (feature 3 > 75.23)
     If (feature 0 <= 21.42)
      If (feature 0 <= 17.84)
       Predict: -0.11457026696795661
      Else (feature 0 > 17.84)
       Predict: 0.9995406591682215
     Else (feature 0 > 21.42)
      If (feature 0 <= 23.02)
       Predict: -2.664637163988949
      Else (feature 0 > 23.02)
       Predict: -0.5023743568762508
  Tree 41 (weight 0.1):
    If (feature 2 <= 1001.9)
     If (feature 1 <= 39.13)
      If (feature 3 <= 79.95)
       Predict: 9.0188365708008
      Else (feature 3 > 79.95)
       Predict: 2.9702965803786205
     Else (feature 1 > 39.13)
      If (feature 3 <= 63.68)
       Predict: -4.052067945951171
      Else (feature 3 > 63.68)
       Predict: -1.0796516186664176
    Else (feature 2 > 1001.9)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.38)
       Predict: 0.15316006561614587
      Else (feature 0 > 14.38)
       Predict: -3.487291240038168
     Else (feature 0 > 15.33)
      If (feature 1 <= 43.13)
       Predict: 2.5605988792505605
      Else (feature 1 > 43.13)
       Predict: 0.03166127813460667
  Tree 42 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 11.42)
      If (feature 1 <= 38.25)
       Predict: -2.0532785635493065
      Else (feature 1 > 38.25)
       Predict: 0.4665697970110133
     Else (feature 0 > 11.42)
      If (feature 1 <= 44.2)
       Predict: -4.178641719198364
      Else (feature 1 > 44.2)
       Predict: -9.84024023297988
    Else (feature 0 > 11.95)
     If (feature 0 <= 13.08)
      If (feature 1 <= 40.89)
       Predict: 4.383821312183712
      Else (feature 1 > 40.89)
       Predict: 2.000819554066434
     Else (feature 0 > 13.08)
      If (feature 0 <= 15.33)
       Predict: -1.0813581518144955
      Else (feature 0 > 15.33)
       Predict: 0.11492139312962121
  Tree 43 (weight 0.1):
    If (feature 0 <= 8.75)
     If (feature 0 <= 7.97)
      If (feature 3 <= 86.54)
       Predict: 0.983392336251922
      Else (feature 3 > 86.54)
       Predict: -0.8690504742953818
     Else (feature 0 > 7.97)
      If (feature 3 <= 62.1)
       Predict: -20.310342278835464
      Else (feature 3 > 62.1)
       Predict: -2.975869736741497
    Else (feature 0 > 8.75)
     If (feature 0 <= 9.42)
      If (feature 2 <= 1015.45)
       Predict: 5.74314556767472
      Else (feature 2 > 1015.45)
       Predict: 2.1033141679659995
     Else (feature 0 > 9.42)
      If (feature 1 <= 40.89)
       Predict: 0.6933339562649613
      Else (feature 1 > 40.89)
       Predict: -0.10718368674776323
  Tree 44 (weight 0.1):
    If (feature 1 <= 74.87)
     If (feature 1 <= 71.43)
      If (feature 1 <= 68.3)
       Predict: -0.0751396787352361
      Else (feature 1 > 68.3)
       Predict: 1.0387569941322914
     Else (feature 1 > 71.43)
      If (feature 1 <= 72.86)
       Predict: -2.5461711201599986
      Else (feature 1 > 72.86)
       Predict: -0.0018936704520639966
    Else (feature 1 > 74.87)
     If (feature 1 <= 77.3)
      If (feature 3 <= 73.33)
       Predict: 3.4362919081871732
      Else (feature 3 > 73.33)
       Predict: 0.022595797531833054
     Else (feature 1 > 77.3)
      If (feature 2 <= 1012.39)
       Predict: -2.0026738842740444
      Else (feature 2 > 1012.39)
       Predict: 1.7553499174736846
  Tree 45 (weight 0.1):
    If (feature 2 <= 1005.35)
     If (feature 1 <= 72.24)
      If (feature 1 <= 59.14)
       Predict: 0.030127466104975898
      Else (feature 1 > 59.14)
       Predict: -2.2341894812350676
     Else (feature 1 > 72.24)
      If (feature 3 <= 60.09)
       Predict: 4.41863108135717
      Else (feature 3 > 60.09)
       Predict: -0.11040726869235623
    Else (feature 2 > 1005.35)
     If (feature 0 <= 31.8)
      If (feature 1 <= 66.25)
       Predict: -0.06640264597455495
      Else (feature 1 > 66.25)
       Predict: 0.6711276381424462
     Else (feature 0 > 31.8)
      If (feature 1 <= 62.44)
       Predict: 18.071299971628946
      Else (feature 1 > 62.44)
       Predict: -1.613111097205577
  Tree 46 (weight 0.1):
    If (feature 0 <= 25.95)
     If (feature 0 <= 23.02)
      If (feature 0 <= 22.6)
       Predict: 0.0037802976144726266
      Else (feature 0 > 22.6)
       Predict: -3.2702083989998565
     Else (feature 0 > 23.02)
      If (feature 1 <= 47.83)
       Predict: 7.351532379664369
      Else (feature 1 > 47.83)
       Predict: 0.6617643737173495
    Else (feature 0 > 25.95)
     If (feature 3 <= 62.1)
      If (feature 0 <= 29.89)
       Predict: 0.7522949567047181
      Else (feature 0 > 29.89)
       Predict: -0.5659530686126862
     Else (feature 3 > 62.1)
      If (feature 1 <= 43.41)
       Predict: -9.179671352130104
      Else (feature 1 > 43.41)
       Predict: -0.9646184420761758
  Tree 47 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 38.62)
      If (feature 3 <= 77.17)
       Predict: -4.215696425771664
      Else (feature 3 > 77.17)
       Predict: 5.655069692148392
     Else (feature 1 > 38.62)
      If (feature 1 <= 39.13)
       Predict: -12.269101167501105
      Else (feature 1 > 39.13)
       Predict: 1.081763483601667
    Else (feature 0 > 5.18)
     If (feature 0 <= 8.75)
      If (feature 0 <= 7.97)
       Predict: -0.19756946285599916
      Else (feature 0 > 7.97)
       Predict: -2.7184931590940438
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.42)
       Predict: 2.558566383813981
      Else (feature 0 > 9.42)
       Predict: -0.006722635545763743
  Tree 48 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 2 <= 1010.89)
      If (feature 1 <= 66.93)
       Predict: -0.7473456438858288
      Else (feature 1 > 66.93)
       Predict: 0.34762458916260297
     Else (feature 2 > 1010.89)
      If (feature 1 <= 58.86)
       Predict: 0.4001213596367478
      Else (feature 1 > 58.86)
       Predict: -0.33373941983121597
    Else (feature 2 > 1028.38)
     If (feature 1 <= 42.85)
      If (feature 1 <= 39.48)
       Predict: 2.1904388134214514
      Else (feature 1 > 39.48)
       Predict: -3.2474441160938956
     Else (feature 1 > 42.85)
      If (feature 3 <= 71.55)
       Predict: -1.061140549595708
      Else (feature 3 > 71.55)
       Predict: 6.934556118848832
  Tree 49 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 10.74)
      If (feature 0 <= 8.75)
       Predict: -0.48190999213172564
      Else (feature 0 > 8.75)
       Predict: 1.0350335598803566
     Else (feature 0 > 10.74)
      If (feature 2 <= 1024.3)
       Predict: -3.057989388513731
      Else (feature 2 > 1024.3)
       Predict: 2.162024696272738
    Else (feature 0 > 11.95)
     If (feature 0 <= 12.5)
      If (feature 3 <= 86.91)
       Predict: 4.627051067913808
      Else (feature 3 > 86.91)
       Predict: 0.9386052167341327
     Else (feature 0 > 12.5)
      If (feature 1 <= 37.8)
       Predict: 4.0889321278523685
      Else (feature 1 > 37.8)
       Predict: -0.02245818963891235
  Tree 50 (weight 0.1):
    If (feature 2 <= 1017.42)
     If (feature 2 <= 1014.19)
      If (feature 1 <= 43.13)
       Predict: 0.9320375696962719
      Else (feature 1 > 43.13)
       Predict: -0.31844348507047093
     Else (feature 2 > 1014.19)
      If (feature 1 <= 42.42)
       Predict: -0.5988031510673222
      Else (feature 1 > 42.42)
       Predict: 1.3187243855742212
    Else (feature 2 > 1017.42)
     If (feature 2 <= 1019.23)
      If (feature 1 <= 44.2)
       Predict: -2.0646082455368195
      Else (feature 1 > 44.2)
       Predict: -0.4969601265683861
     Else (feature 2 > 1019.23)
      If (feature 0 <= 17.84)
       Predict: -0.2870181057370213
      Else (feature 0 > 17.84)
       Predict: 2.6148230736448608
  Tree 51 (weight 0.1):
    If (feature 1 <= 38.62)
     If (feature 0 <= 18.4)
      If (feature 0 <= 5.18)
       Predict: 3.850885339006515
      Else (feature 0 > 5.18)
       Predict: -0.940687510645146
     Else (feature 0 > 18.4)
      If (feature 0 <= 18.98)
       Predict: -10.80330040562501
      Else (feature 0 > 18.98)
       Predict: -18.03404880535599
    Else (feature 1 > 38.62)
     If (feature 2 <= 1026.23)
      If (feature 0 <= 13.56)
       Predict: 0.5295719576334972
      Else (feature 0 > 13.56)
       Predict: -0.052812717813551166
     Else (feature 2 > 1026.23)
      If (feature 1 <= 40.22)
       Predict: -4.371246083031292
      Else (feature 1 > 40.22)
       Predict: -1.3541229527292618
  Tree 52 (weight 0.1):
    If (feature 1 <= 66.25)
     If (feature 1 <= 64.84)
      If (feature 3 <= 41.26)
       Predict: 3.045631536773922
      Else (feature 3 > 41.26)
       Predict: -0.0337837562463145
     Else (feature 1 > 64.84)
      If (feature 1 <= 65.27)
       Predict: -5.921444872611693
      Else (feature 1 > 65.27)
       Predict: -0.8270282146869598
    Else (feature 1 > 66.25)
     If (feature 0 <= 23.02)
      If (feature 0 <= 19.83)
       Predict: 1.5405239234096135
      Else (feature 0 > 19.83)
       Predict: -3.1288830506195398
     Else (feature 0 > 23.02)
      If (feature 0 <= 25.35)
       Predict: 3.2672442442602656
      Else (feature 0 > 25.35)
       Predict: -0.007592990267182966
  Tree 53 (weight 0.1):
    If (feature 0 <= 17.84)
     If (feature 1 <= 46.93)
      If (feature 0 <= 17.2)
       Predict: 0.1228349542857993
      Else (feature 0 > 17.2)
       Predict: -2.392588492043597
     Else (feature 1 > 46.93)
      If (feature 2 <= 1020.77)
       Predict: -1.8240349072310669
      Else (feature 2 > 1020.77)
       Predict: -6.523289398433308
    Else (feature 0 > 17.84)
     If (feature 0 <= 18.4)
      If (feature 1 <= 47.83)
       Predict: 0.5318997435908227
      Else (feature 1 > 47.83)
       Predict: 4.907584149653537
     Else (feature 0 > 18.4)
      If (feature 1 <= 46.93)
       Predict: -2.110133253015907
      Else (feature 1 > 46.93)
       Predict: 0.20708863671712482
  Tree 54 (weight 0.1):
    If (feature 3 <= 76.79)
     If (feature 1 <= 40.05)
      If (feature 1 <= 39.96)
       Predict: -0.7416033424896232
      Else (feature 1 > 39.96)
       Predict: -6.880323474190146
     Else (feature 1 > 40.05)
      If (feature 1 <= 40.89)
       Predict: 2.887497917363201
      Else (feature 1 > 40.89)
       Predict: 0.17777582956662522
    Else (feature 3 > 76.79)
     If (feature 0 <= 19.61)
      If (feature 0 <= 17.84)
       Predict: -0.09172434324104897
      Else (feature 0 > 17.84)
       Predict: 1.9482862934683598
     Else (feature 0 > 19.61)
      If (feature 2 <= 1010.6)
       Predict: -0.15262790703036064
      Else (feature 2 > 1010.6)
       Predict: -1.7280878096087295
  Tree 55 (weight 0.1):
    If (feature 0 <= 24.79)
     If (feature 0 <= 23.02)
      If (feature 1 <= 66.93)
       Predict: 0.02682576814507517
      Else (feature 1 > 66.93)
       Predict: -2.323863726560255
     Else (feature 0 > 23.02)
      If (feature 1 <= 47.83)
       Predict: 6.909290893058579
      Else (feature 1 > 47.83)
       Predict: 0.9944889736997976
    Else (feature 0 > 24.79)
     If (feature 3 <= 65.24)
      If (feature 0 <= 28.5)
       Predict: 0.8432916332803679
      Else (feature 0 > 28.5)
       Predict: -0.3680864130080106
     Else (feature 3 > 65.24)
      If (feature 1 <= 66.51)
       Predict: -2.1147474860288
      Else (feature 1 > 66.51)
       Predict: -0.3834883036951788
  Tree 56 (weight 0.1):
    If (feature 0 <= 15.33)
     If (feature 0 <= 14.38)
      If (feature 0 <= 11.95)
       Predict: -0.3290262091199092
      Else (feature 0 > 11.95)
       Predict: 0.8543511625463592
     Else (feature 0 > 14.38)
      If (feature 2 <= 1016.21)
       Predict: -0.7208476709379852
      Else (feature 2 > 1016.21)
       Predict: -4.40928839539672
    Else (feature 0 > 15.33)
     If (feature 0 <= 16.22)
      If (feature 2 <= 1013.19)
       Predict: 4.554268903891635
      Else (feature 2 > 1013.19)
       Predict: 1.538781048856137
     Else (feature 0 > 16.22)
      If (feature 1 <= 46.93)
       Predict: -1.1488437756174756
      Else (feature 1 > 46.93)
       Predict: 0.1634274865006602
  Tree 57 (weight 0.1):
    If (feature 2 <= 1007.46)
     If (feature 1 <= 73.67)
      If (feature 1 <= 71.43)
       Predict: -0.28457458674767294
      Else (feature 1 > 71.43)
       Predict: -2.556284198496123
     Else (feature 1 > 73.67)
      If (feature 3 <= 60.81)
       Predict: 4.31886476056719
      Else (feature 3 > 60.81)
       Predict: 0.3197495651743129
    Else (feature 2 > 1007.46)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.04575453109929229
      Else (feature 1 > 46.93)
       Predict: -2.141138284310683
     Else (feature 0 > 17.84)
      If (feature 1 <= 56.57)
       Predict: 1.3439965861050847
      Else (feature 1 > 56.57)
       Predict: -0.02904919315788331
  Tree 58 (weight 0.1):
    If (feature 0 <= 31.8)
     If (feature 1 <= 66.25)
      If (feature 1 <= 64.84)
       Predict: -0.006836636445003446
      Else (feature 1 > 64.84)
       Predict: -2.0890363043188134
     Else (feature 1 > 66.25)
      If (feature 1 <= 69.05)
       Predict: 1.8596834938858298
      Else (feature 1 > 69.05)
       Predict: -0.2637818907162569
    Else (feature 0 > 31.8)
     If (feature 1 <= 69.34)
      If (feature 2 <= 1009.63)
       Predict: -4.53407923927751
      Else (feature 2 > 1009.63)
       Predict: 1.2479530412848983
     Else (feature 1 > 69.34)
      If (feature 1 <= 69.88)
       Predict: 5.672382101944148
      Else (feature 1 > 69.88)
       Predict: -0.7728960613425813
  Tree 59 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 68.3)
      If (feature 1 <= 43.41)
       Predict: 0.423961936091299
      Else (feature 1 > 43.41)
       Predict: -1.0411314850417004
     Else (feature 1 > 68.3)
      If (feature 1 <= 68.67)
       Predict: 7.130757445704555
      Else (feature 1 > 68.67)
       Predict: 0.1160942217864609
    Else (feature 2 > 1010.89)
     If (feature 3 <= 93.63)
      If (feature 1 <= 58.86)
       Predict: 0.41091291246834866
      Else (feature 1 > 58.86)
       Predict: -0.2764637915143923
     Else (feature 3 > 93.63)
      If (feature 1 <= 41.74)
       Predict: -3.564757715833512
      Else (feature 1 > 41.74)
       Predict: 1.1644353912440248
  Tree 60 (weight 0.1):
    If (feature 1 <= 48.6)
     If (feature 1 <= 44.88)
      If (feature 2 <= 1016.57)
       Predict: 0.4410572983039277
      Else (feature 2 > 1016.57)
       Predict: -0.44414793681792664
     Else (feature 1 > 44.88)
      If (feature 2 <= 1014.35)
       Predict: -3.0626378082153085
      Else (feature 2 > 1014.35)
       Predict: 2.0328536525605063
    Else (feature 1 > 48.6)
     If (feature 1 <= 52.05)
      If (feature 2 <= 1009.9)
       Predict: 0.24004783900051171
      Else (feature 2 > 1009.9)
       Predict: 3.1645061792332916
     Else (feature 1 > 52.05)
      If (feature 0 <= 17.84)
       Predict: -1.95074879327582
      Else (feature 0 > 17.84)
       Predict: 0.021106826304965107
  Tree 61 (weight 0.1):
    If (feature 1 <= 74.87)
     If (feature 1 <= 71.43)
      If (feature 1 <= 68.3)
       Predict: -0.06241270845694165
      Else (feature 1 > 68.3)
       Predict: 0.8051320337219834
     Else (feature 1 > 71.43)
      If (feature 0 <= 24.57)
       Predict: 1.648459594873699
      Else (feature 0 > 24.57)
       Predict: -1.2314608832462137
    Else (feature 1 > 74.87)
     If (feature 1 <= 77.3)
      If (feature 0 <= 21.42)
       Predict: -7.482222216002697
      Else (feature 0 > 21.42)
       Predict: 1.8228183337802573
     Else (feature 1 > 77.3)
      If (feature 2 <= 1012.39)
       Predict: -1.4326641812285505
      Else (feature 2 > 1012.39)
       Predict: 1.7079353624089986
  Tree 62 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 42.07)
      If (feature 3 <= 96.38)
       Predict: 1.4583097259406885
      Else (feature 3 > 96.38)
       Predict: 7.4053761713858615
     Else (feature 1 > 42.07)
      If (feature 2 <= 1008.19)
       Predict: 0.311290850436914
      Else (feature 2 > 1008.19)
       Predict: -5.145119802972147
    Else (feature 0 > 5.18)
     If (feature 1 <= 38.62)
      If (feature 0 <= 18.4)
       Predict: -0.7259884411546618
      Else (feature 0 > 18.4)
       Predict: -12.427884135864616
     Else (feature 1 > 38.62)
      If (feature 1 <= 39.48)
       Predict: 1.131291291234381
      Else (feature 1 > 39.48)
       Predict: -0.007004055574359982
  Tree 63 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 70.8)
      If (feature 1 <= 69.05)
       Predict: -0.45566718124370104
      Else (feature 1 > 69.05)
       Predict: -3.3633539333883373
     Else (feature 1 > 70.8)
      If (feature 3 <= 70.63)
       Predict: 1.7061073842258219
      Else (feature 3 > 70.63)
       Predict: -0.35469491259927843
    Else (feature 2 > 1004.52)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.13)
       Predict: 0.13165022513417465
      Else (feature 0 > 14.13)
       Predict: -1.8886218519887454
     Else (feature 0 > 15.33)
      If (feature 1 <= 43.13)
       Predict: 2.0897911694212086
      Else (feature 1 > 43.13)
       Predict: 0.023571622513158218
  Tree 64 (weight 0.1):
    If (feature 1 <= 41.92)
     If (feature 1 <= 41.58)
      If (feature 2 <= 1015.45)
       Predict: 0.6420804366913081
      Else (feature 2 > 1015.45)
       Predict: -0.3393001000428116
     Else (feature 1 > 41.58)
      If (feature 3 <= 91.38)
       Predict: -2.959889489145066
      Else (feature 3 > 91.38)
       Predict: -14.822621379271645
    Else (feature 1 > 41.92)
     If (feature 1 <= 43.13)
      If (feature 0 <= 15.33)
       Predict: 0.5584851317693598
      Else (feature 0 > 15.33)
       Predict: 5.35806974907062
     Else (feature 1 > 43.13)
      If (feature 1 <= 43.65)
       Predict: -2.5734171913252673
      Else (feature 1 > 43.65)
       Predict: 0.06206747847844893
  Tree 65 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 66.93)
      If (feature 0 <= 20.6)
       Predict: -0.0679333275254979
      Else (feature 0 > 20.6)
       Predict: -1.053808811058633
     Else (feature 1 > 66.93)
      If (feature 1 <= 67.32)
       Predict: 7.372080266725638
      Else (feature 1 > 67.32)
       Predict: 0.09996335027123535
    Else (feature 2 > 1010.89)
     If (feature 3 <= 75.61)
      If (feature 1 <= 40.05)
       Predict: -0.9831581524231143
      Else (feature 1 > 40.05)
       Predict: 0.5486160789249349
     Else (feature 3 > 75.61)
      If (feature 1 <= 58.86)
       Predict: 0.19399224442246701
      Else (feature 1 > 58.86)
       Predict: -1.5652059699408227
  Tree 66 (weight 0.1):
    If (feature 0 <= 28.75)
     If (feature 1 <= 73.18)
      If (feature 1 <= 71.43)
       Predict: 0.05143978594106816
      Else (feature 1 > 71.43)
       Predict: -1.436513600322334
     Else (feature 1 > 73.18)
      If (feature 3 <= 73.33)
       Predict: 4.1459864582084975
      Else (feature 3 > 73.33)
       Predict: 0.34965185037807356
    Else (feature 0 > 28.75)
     If (feature 2 <= 1014.54)
      If (feature 2 <= 1013.43)
       Predict: -0.4008005884834272
      Else (feature 2 > 1013.43)
       Predict: 3.683818693727259
     Else (feature 2 > 1014.54)
      If (feature 1 <= 67.83)
       Predict: -0.82614879352537
      Else (feature 1 > 67.83)
       Predict: -4.535981326886069
  Tree 67 (weight 0.1):
    If (feature 1 <= 47.83)
     If (feature 0 <= 23.02)
      If (feature 0 <= 18.71)
       Predict: -0.0010074123242523121
      Else (feature 0 > 18.71)
       Predict: -3.2926535011699234
     Else (feature 0 > 23.02)
      If (feature 2 <= 1012.39)
       Predict: 1.3034696914565052
      Else (feature 2 > 1012.39)
       Predict: 11.235282784300427
    Else (feature 1 > 47.83)
     If (feature 1 <= 56.57)
      If (feature 0 <= 17.84)
       Predict: -1.039931035628621
      Else (feature 0 > 17.84)
       Predict: 1.9905896386111916
     Else (feature 1 > 56.57)
      If (feature 1 <= 57.19)
       Predict: -2.3357601760278204
      Else (feature 1 > 57.19)
       Predict: -0.0355403353056693
  Tree 68 (weight 0.1):
    If (feature 0 <= 24.79)
     If (feature 3 <= 41.26)
      If (feature 1 <= 45.87)
       Predict: 2.4904273637383265
      Else (feature 1 > 45.87)
       Predict: 13.013875696314063
     Else (feature 3 > 41.26)
      If (feature 1 <= 49.02)
       Predict: -0.18642415027276396
      Else (feature 1 > 49.02)
       Predict: 0.47121076166963227
    Else (feature 0 > 24.79)
     If (feature 1 <= 65.27)
      If (feature 1 <= 64.84)
       Predict: -0.5...

Conclusion

Wow! So our best model is in fact our Gradient Boosted Decision tree model which uses an ensemble of 120 Trees with a depth of 3 to construct a better model than the single decision tree.

Persisting Statistical Machine Learning Models

Let's save our best model so we can load it without having to rerun the validation and training again.

gbtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[GBTRegressionModel]
        .write.overwrite().save("dbfs:///databricks/driver/MyTrainedGbtModel")

val sameModel = GBTRegressionModel.load("dbfs:///databricks/driver/MyTrainedGbtModel/")

sameModel: org.apache.spark.ml.regression.GBTRegressionModel = GBTRegressionModel (uid=gbtr_9c5ab45fe584) with 120 trees

// making sure we have the same model loaded from the file
sameModel.toDebugString

res53: String =
"GBTRegressionModel (uid=gbtr_9c5ab45fe584) with 120 trees
  Tree 0 (weight 1.0):
    If (feature 0 <= 17.84)
     If (feature 0 <= 11.95)
      If (feature 0 <= 8.75)
       Predict: 483.5412151067323
      Else (feature 0 > 8.75)
       Predict: 475.6305502392345
     Else (feature 0 > 11.95)
      If (feature 0 <= 15.33)
       Predict: 467.63141917293234
      Else (feature 0 > 15.33)
       Predict: 460.74754125412574
    Else (feature 0 > 17.84)
     If (feature 0 <= 23.02)
      If (feature 1 <= 47.83)
       Predict: 457.1077966101695
      Else (feature 1 > 47.83)
       Predict: 448.74750213858016
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: 442.88544855967086
      Else (feature 1 > 66.25)
       Predict: 434.7293710691822
  Tree 1 (weight 0.1):
    If (feature 2 <= 1009.9)
     If (feature 1 <= 43.13)
      If (feature 0 <= 15.33)
       Predict: -0.31094207231231485
      Else (feature 0 > 15.33)
       Predict: 4.302958436537365
     Else (feature 1 > 43.13)
      If (feature 0 <= 23.02)
       Predict: -8.38392506141353
      Else (feature 0 > 23.02)
       Predict: -2.399960976520273
    Else (feature 2 > 1009.9)
     If (feature 3 <= 86.21)
      If (feature 0 <= 26.35)
       Predict: 2.888623754019027
      Else (feature 0 > 26.35)
       Predict: -1.1489483044194229
     Else (feature 3 > 86.21)
      If (feature 1 <= 39.72)
       Predict: 3.876324424163314
      Else (feature 1 > 39.72)
       Predict: -3.058952828112949
  Tree 2 (weight 0.1):
    If (feature 2 <= 1009.63)
     If (feature 1 <= 43.13)
      If (feature 0 <= 11.95)
       Predict: -1.4091086031845625
      Else (feature 0 > 11.95)
       Predict: 2.6329466235800942
     Else (feature 1 > 43.13)
      If (feature 0 <= 23.02)
       Predict: -6.795414480322956
      Else (feature 0 > 23.02)
       Predict: -2.166560698742912
    Else (feature 2 > 1009.63)
     If (feature 3 <= 80.44)
      If (feature 0 <= 26.98)
       Predict: 2.878622882275939
      Else (feature 0 > 26.98)
       Predict: -1.146426969990865
     Else (feature 3 > 80.44)
      If (feature 3 <= 94.55)
       Predict: -0.35885921725905906
      Else (feature 3 > 94.55)
       Predict: -5.75364586186002
  Tree 3 (weight 0.1):
    If (feature 0 <= 27.6)
     If (feature 3 <= 70.2)
      If (feature 1 <= 40.05)
       Predict: -0.9480831286616939
      Else (feature 1 > 40.05)
       Predict: 3.660397090904016
     Else (feature 3 > 70.2)
      If (feature 1 <= 40.64)
       Predict: 2.1539405832035627
      Else (feature 1 > 40.64)
       Predict: -1.2281619807661366
    Else (feature 0 > 27.6)
     If (feature 1 <= 65.27)
      If (feature 2 <= 1005.99)
       Predict: -15.33433697033558
      Else (feature 2 > 1005.99)
       Predict: -5.866095468145647
     Else (feature 1 > 65.27)
      If (feature 2 <= 1008.75)
       Predict: -4.03431044067007
      Else (feature 2 > 1008.75)
       Predict: -0.23440867445577207
  Tree 4 (weight 0.1):
    If (feature 0 <= 26.35)
     If (feature 0 <= 23.02)
      If (feature 1 <= 68.67)
       Predict: 0.12035773384797814
      Else (feature 1 > 68.67)
       Predict: -13.928523073642005
     Else (feature 0 > 23.02)
      If (feature 0 <= 24.57)
       Predict: 5.5622340839882165
      Else (feature 0 > 24.57)
       Predict: 1.6938172370244715
    Else (feature 0 > 26.35)
     If (feature 1 <= 66.25)
      If (feature 2 <= 1008.4)
       Predict: -9.009916879825393
      Else (feature 2 > 1008.4)
       Predict: -3.059736394918022
     Else (feature 1 > 66.25)
      If (feature 0 <= 30.2)
       Predict: 0.14704705100738577
      Else (feature 0 > 30.2)
       Predict: -3.2914123948921006
  Tree 5 (weight 0.1):
    If (feature 2 <= 1010.41)
     If (feature 1 <= 43.41)
      If (feature 3 <= 99.27)
       Predict: 1.2994444710077233
      Else (feature 3 > 99.27)
       Predict: -6.649548317319231
     Else (feature 1 > 43.41)
      If (feature 0 <= 23.02)
       Predict: -4.9119452777748
      Else (feature 0 > 23.02)
       Predict: -0.9514185089440673
    Else (feature 2 > 1010.41)
     If (feature 3 <= 89.83)
      If (feature 0 <= 31.26)
       Predict: 1.2914123584761403
      Else (feature 0 > 31.26)
       Predict: -5.115001417285994
     Else (feature 3 > 89.83)
      If (feature 1 <= 40.64)
       Predict: 1.5160976219176363
      Else (feature 1 > 40.64)
       Predict: -4.202813699523934
  Tree 6 (weight 0.1):
    If (feature 2 <= 1007.27)
     If (feature 0 <= 27.94)
      If (feature 3 <= 71.09)
       Predict: 1.616448005210527
      Else (feature 3 > 71.09)
       Predict: -2.1313527108274157
     Else (feature 0 > 27.94)
      If (feature 1 <= 68.3)
       Predict: -8.579840063013142
      Else (feature 1 > 68.3)
       Predict: -1.915909819494233
    Else (feature 2 > 1007.27)
     If (feature 3 <= 95.45)
      If (feature 0 <= 6.52)
       Predict: 4.973465595410054
      Else (feature 0 > 6.52)
       Predict: 0.3837975458985242
     Else (feature 3 > 95.45)
      If (feature 2 <= 1013.43)
       Predict: -0.8175453481344352
      Else (feature 2 > 1013.43)
       Predict: -7.264843604639278
  Tree 7 (weight 0.1):
    If (feature 0 <= 26.35)
     If (feature 3 <= 71.09)
      If (feature 1 <= 67.83)
       Predict: 1.9620965187817083
      Else (feature 1 > 67.83)
       Predict: 7.953863660960779
     Else (feature 3 > 71.09)
      If (feature 1 <= 40.89)
       Predict: 1.2020440154192213
      Else (feature 1 > 40.89)
       Predict: -0.9989659748111419
    Else (feature 0 > 26.35)
     If (feature 1 <= 66.25)
      If (feature 2 <= 1008.4)
       Predict: -6.230272922553423
      Else (feature 2 > 1008.4)
       Predict: -2.654681371247991
     Else (feature 1 > 66.25)
      If (feature 2 <= 1004.52)
       Predict: -3.9527797601131853
      Else (feature 2 > 1004.52)
       Predict: -0.21770148036273387
  Tree 8 (weight 0.1):
    If (feature 0 <= 29.56)
     If (feature 3 <= 63.16)
      If (feature 1 <= 72.24)
       Predict: 1.9612116105231265
      Else (feature 1 > 72.24)
       Predict: 8.756949826030025
     Else (feature 3 > 63.16)
      If (feature 0 <= 5.95)
       Predict: 4.445363585074405
      Else (feature 0 > 5.95)
       Predict: -0.4097996897633835
    Else (feature 0 > 29.56)
     If (feature 1 <= 68.3)
      If (feature 2 <= 1009.9)
       Predict: -7.882200867406393
      Else (feature 2 > 1009.9)
       Predict: -1.7273221348184091
     Else (feature 1 > 68.3)
      If (feature 2 <= 1013.77)
       Predict: -0.7219749804525829
      Else (feature 2 > 1013.77)
       Predict: -6.492100849806538
  Tree 9 (weight 0.1):
    If (feature 3 <= 89.83)
     If (feature 0 <= 25.72)
      If (feature 0 <= 23.02)
       Predict: 0.15450088997272685
      Else (feature 0 > 23.02)
       Predict: 3.010254802875794
     Else (feature 0 > 25.72)
      If (feature 1 <= 66.25)
       Predict: -2.5821765284417615
      Else (feature 1 > 66.25)
       Predict: -0.3935112713804148
    Else (feature 3 > 89.83)
     If (feature 2 <= 1019.52)
      If (feature 0 <= 7.08)
       Predict: 3.264389020443774
      Else (feature 0 > 7.08)
       Predict: -1.6246048211383168
     Else (feature 2 > 1019.52)
      If (feature 0 <= 8.75)
       Predict: -8.005340799169343
      Else (feature 0 > 8.75)
       Predict: -2.9832409167030063
  Tree 10 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 0 <= 17.84)
      If (feature 1 <= 45.87)
       Predict: 0.26309432916452813
      Else (feature 1 > 45.87)
       Predict: -5.716473785544373
     Else (feature 0 > 17.84)
      If (feature 2 <= 1012.56)
       Predict: -0.15863259341493433
      Else (feature 2 > 1012.56)
       Predict: 7.899625065937478
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 3 <= 67.72)
       Predict: -27.101084325134025
      Else (feature 3 > 67.72)
       Predict: -12.755339130015875
     Else (feature 0 > 17.84)
      If (feature 0 <= 20.6)
       Predict: 3.8741798886113408
      Else (feature 0 > 20.6)
       Predict: -0.8179571837367839
  Tree 11 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 74.22)
      If (feature 1 <= 59.14)
       Predict: -0.6678644068375302
      Else (feature 1 > 59.14)
       Predict: -5.0251736913870495
     Else (feature 1 > 74.22)
      If (feature 2 <= 1000.68)
       Predict: -1.9453153753750236
      Else (feature 2 > 1000.68)
       Predict: 3.954565899065237
    Else (feature 2 > 1004.52)
     If (feature 3 <= 60.81)
      If (feature 0 <= 29.27)
       Predict: 2.256991118214201
      Else (feature 0 > 29.27)
       Predict: -0.8956432652281918
     Else (feature 3 > 60.81)
      If (feature 0 <= 5.18)
       Predict: 5.30208686561611
      Else (feature 0 > 5.18)
       Predict: -0.2275806642044292
  Tree 12 (weight 0.1):
    If (feature 3 <= 93.63)
     If (feature 0 <= 20.6)
      If (feature 0 <= 17.84)
       Predict: -0.13650451477274114
      Else (feature 0 > 17.84)
       Predict: 4.26138638419226
     Else (feature 0 > 20.6)
      If (feature 0 <= 23.02)
       Predict: -4.145788149131118
      Else (feature 0 > 23.02)
       Predict: 0.45010060784860767
    Else (feature 3 > 93.63)
     If (feature 0 <= 11.95)
      If (feature 0 <= 6.52)
       Predict: 1.9630864105825856
      Else (feature 0 > 6.52)
       Predict: -5.847103580294793
     Else (feature 0 > 11.95)
      If (feature 1 <= 57.85)
       Predict: 1.6850763767018282
      Else (feature 1 > 57.85)
       Predict: -3.57522814358917
  Tree 13 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.39)
      If (feature 0 <= 13.56)
       Predict: 0.7497248523199469
      Else (feature 0 > 13.56)
       Predict: -0.8096048572768345
     Else (feature 1 > 49.39)
      If (feature 0 <= 17.84)
       Predict: -4.9975868045736025
      Else (feature 0 > 17.84)
       Predict: 6.70181838603398
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 1 <= 58.62)
       Predict: -8.139327595464518
      Else (feature 1 > 58.62)
       Predict: -11.260696586956563
     Else (feature 0 > 17.84)
      If (feature 2 <= 1020.32)
       Predict: -0.4173502593107514
      Else (feature 2 > 1020.32)
       Predict: 7.350524302545053
  Tree 14 (weight 0.1):
    If (feature 2 <= 1009.3)
     If (feature 1 <= 73.67)
      If (feature 0 <= 26.35)
       Predict: -0.2834715308768144
      Else (feature 0 > 26.35)
       Predict: -2.2855655986052446
     Else (feature 1 > 73.67)
      If (feature 0 <= 21.42)
       Predict: -19.886551554013977
      Else (feature 0 > 21.42)
       Predict: 1.8345107899392203
    Else (feature 2 > 1009.3)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.2012146645141011
      Else (feature 1 > 46.93)
       Predict: -5.331252849501989
     Else (feature 0 > 17.84)
      If (feature 0 <= 20.6)
       Predict: 3.9009310043506518
      Else (feature 0 > 20.6)
       Predict: 0.05492627340134294
  Tree 15 (weight 0.1):
    If (feature 3 <= 80.44)
     If (feature 0 <= 26.57)
      If (feature 0 <= 23.02)
       Predict: 0.24935555983937532
      Else (feature 0 > 23.02)
       Predict: 1.9734839371689987
     Else (feature 0 > 26.57)
      If (feature 1 <= 66.25)
       Predict: -2.652691255012269
      Else (feature 1 > 66.25)
       Predict: 0.10205623249441657
    Else (feature 3 > 80.44)
     If (feature 1 <= 57.85)
      If (feature 2 <= 1021.65)
       Predict: 0.3189331596273633
      Else (feature 2 > 1021.65)
       Predict: -2.493847422724499
     Else (feature 1 > 57.85)
      If (feature 0 <= 23.02)
       Predict: -4.443277995263894
      Else (feature 0 > 23.02)
       Predict: 1.0414575062489446
  Tree 16 (weight 0.1):
    If (feature 0 <= 6.52)
     If (feature 3 <= 67.72)
      If (feature 1 <= 39.48)
       Predict: -0.021931809818089017
      Else (feature 1 > 39.48)
       Predict: 17.644618798102908
     Else (feature 3 > 67.72)
      If (feature 1 <= 42.07)
       Predict: 2.6927240976688487
      Else (feature 1 > 42.07)
       Predict: -3.720328734281554
    Else (feature 0 > 6.52)
     If (feature 0 <= 8.75)
      If (feature 0 <= 7.97)
       Predict: -1.1870026837027776
      Else (feature 0 > 7.97)
       Predict: -6.311604790035118
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.73)
       Predict: 5.036277690956247
      Else (feature 0 > 9.73)
       Predict: -0.07156864179175153
  Tree 17 (weight 0.1):
    If (feature 2 <= 1005.35)
     If (feature 1 <= 70.8)
      If (feature 0 <= 21.14)
       Predict: 0.2557898848412102
      Else (feature 0 > 21.14)
       Predict: -4.092246463553751
     Else (feature 1 > 70.8)
      If (feature 0 <= 23.02)
       Predict: -17.7762740471523
      Else (feature 0 > 23.02)
       Predict: 1.4679036019616782
    Else (feature 2 > 1005.35)
     If (feature 3 <= 60.81)
      If (feature 2 <= 1021.17)
       Predict: 0.8109918761137652
      Else (feature 2 > 1021.17)
       Predict: 6.491756407811347
     Else (feature 3 > 60.81)
      If (feature 0 <= 25.72)
       Predict: 0.06495066055048145
      Else (feature 0 > 25.72)
       Predict: -1.234843690619109
  Tree 18 (weight 0.1):
    If (feature 3 <= 93.63)
     If (feature 0 <= 13.56)
      If (feature 0 <= 11.95)
       Predict: -0.1389635939018028
      Else (feature 0 > 11.95)
       Predict: 4.085304226900187
     Else (feature 0 > 13.56)
      If (feature 0 <= 15.33)
       Predict: -3.558076811842663
      Else (feature 0 > 15.33)
       Predict: 0.24840255719067195
    Else (feature 3 > 93.63)
     If (feature 0 <= 11.95)
      If (feature 0 <= 6.52)
       Predict: 1.1725211739721944
      Else (feature 0 > 6.52)
       Predict: -4.696815201291802
     Else (feature 0 > 11.95)
      If (feature 0 <= 23.42)
       Predict: -0.1435586215485262
      Else (feature 0 > 23.42)
       Predict: 6.017267110381734
  Tree 19 (weight 0.1):
    If (feature 0 <= 29.89)
     If (feature 3 <= 46.38)
      If (feature 2 <= 1020.32)
       Predict: 2.734528637686715
      Else (feature 2 > 1020.32)
       Predict: 14.229272221061546
     Else (feature 3 > 46.38)
      If (feature 1 <= 73.18)
       Predict: -0.09112932077559661
      Else (feature 1 > 73.18)
       Predict: 2.171636618202333
    Else (feature 0 > 29.89)
     If (feature 1 <= 68.3)
      If (feature 2 <= 1012.96)
       Predict: -4.842672386234583
      Else (feature 2 > 1012.96)
       Predict: 0.4656753436410731
     Else (feature 1 > 68.3)
      If (feature 1 <= 69.88)
       Predict: 1.9998755414672877
      Else (feature 1 > 69.88)
       Predict: -1.377187598546301
  Tree 20 (weight 0.1):
    If (feature 1 <= 40.89)
     If (feature 0 <= 11.95)
      If (feature 0 <= 10.74)
       Predict: 0.3474341793041741
      Else (feature 0 > 10.74)
       Predict: -3.2174625433704844
     Else (feature 0 > 11.95)
      If (feature 0 <= 13.56)
       Predict: 6.2521753652461385
      Else (feature 0 > 13.56)
       Predict: 0.7467107076401086
    Else (feature 1 > 40.89)
     If (feature 1 <= 41.16)
      If (feature 2 <= 1011.9)
       Predict: 1.6159428806525291
      Else (feature 2 > 1011.9)
       Predict: -5.525791920129847
     Else (feature 1 > 41.16)
      If (feature 1 <= 41.48)
       Predict: 2.3655609293253264
      Else (feature 1 > 41.48)
       Predict: -0.18730957785387015
  Tree 21 (weight 0.1):
    If (feature 0 <= 7.08)
     If (feature 1 <= 41.58)
      If (feature 1 <= 41.16)
       Predict: 1.9153935195932974
      Else (feature 1 > 41.16)
       Predict: 7.0746807427814735
     Else (feature 1 > 41.58)
      If (feature 2 <= 1020.77)
       Predict: -1.256554177586309
      Else (feature 2 > 1020.77)
       Predict: -26.29941855196938
    Else (feature 0 > 7.08)
     If (feature 0 <= 8.75)
      If (feature 1 <= 37.8)
       Predict: -8.544132394601597
      Else (feature 1 > 37.8)
       Predict: -2.6184141709801976
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.73)
       Predict: 4.069411815161333
      Else (feature 0 > 9.73)
       Predict: -0.06494039395966968
  Tree 22 (weight 0.1):
    If (feature 0 <= 23.02)
     If (feature 0 <= 21.69)
      If (feature 0 <= 15.33)
       Predict: -0.48298234147973435
      Else (feature 0 > 15.33)
       Predict: 1.2747845905419344
     Else (feature 0 > 21.69)
      If (feature 1 <= 66.25)
       Predict: -3.44223180465188
      Else (feature 1 > 66.25)
       Predict: -9.677838572965495
    Else (feature 0 > 23.02)
     If (feature 0 <= 24.39)
      If (feature 1 <= 66.25)
       Predict: 1.4289485230939327
      Else (feature 1 > 66.25)
       Predict: 7.493228657621072
     Else (feature 0 > 24.39)
      If (feature 1 <= 66.25)
       Predict: -1.55164310941819
      Else (feature 1 > 66.25)
       Predict: 0.5159038364280375
  Tree 23 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 66.93)
      If (feature 1 <= 43.41)
       Predict: 0.8366856528539243
      Else (feature 1 > 43.41)
       Predict: -2.146264827541657
     Else (feature 1 > 66.93)
      If (feature 0 <= 23.02)
       Predict: -4.593173040738928
      Else (feature 0 > 23.02)
       Predict: 0.7595925761507126
    Else (feature 2 > 1010.89)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.38)
       Predict: 0.19019050526253845
      Else (feature 0 > 14.38)
       Predict: -4.931089744789576
     Else (feature 0 > 15.33)
      If (feature 1 <= 56.57)
       Predict: 2.893896440054576
      Else (feature 1 > 56.57)
       Predict: -0.2411893147021192
  Tree 24 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 39.13)
      If (feature 0 <= 16.56)
       Predict: 5.674347262101248
      Else (feature 0 > 16.56)
       Predict: -15.35003850200303
     Else (feature 1 > 39.13)
      If (feature 1 <= 70.8)
       Predict: -2.2136597249782484
      Else (feature 1 > 70.8)
       Predict: 0.4854909471410394
    Else (feature 2 > 1004.52)
     If (feature 0 <= 23.02)
      If (feature 0 <= 21.14)
       Predict: 0.25072963079321764
      Else (feature 0 > 21.14)
       Predict: -3.1127381475029745
     Else (feature 0 > 23.02)
      If (feature 0 <= 24.98)
       Predict: 2.513302584995404
      Else (feature 0 > 24.98)
       Predict: -0.17126775916442186
  Tree 25 (weight 0.1):
    If (feature 3 <= 76.79)
     If (feature 0 <= 28.75)
      If (feature 1 <= 66.25)
       Predict: 0.1271610430935476
      Else (feature 1 > 66.25)
       Predict: 2.4600009065275934
     Else (feature 0 > 28.75)
      If (feature 1 <= 44.58)
       Predict: -10.925990145829292
      Else (feature 1 > 44.58)
       Predict: -0.7031644656131009
    Else (feature 3 > 76.79)
     If (feature 0 <= 20.9)
      If (feature 0 <= 17.84)
       Predict: -0.3807566877980857
      Else (feature 0 > 17.84)
       Predict: 2.329590528017136
     Else (feature 0 > 20.9)
      If (feature 0 <= 23.02)
       Predict: -3.741947089345415
      Else (feature 0 > 23.02)
       Predict: -0.3619479813878585
  Tree 26 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 42.07)
      If (feature 3 <= 84.36)
       Predict: 5.869887042156764
      Else (feature 3 > 84.36)
       Predict: 2.3621425360574837
     Else (feature 1 > 42.07)
      If (feature 2 <= 1007.82)
       Predict: -1.4185266335795177
      Else (feature 2 > 1007.82)
       Predict: -5.383717178467172
    Else (feature 0 > 5.18)
     If (feature 3 <= 53.32)
      If (feature 2 <= 1021.17)
       Predict: 0.6349729680247564
      Else (feature 2 > 1021.17)
       Predict: 9.504309080910616
     Else (feature 3 > 53.32)
      If (feature 0 <= 25.95)
       Predict: 0.010243524812335326
      Else (feature 0 > 25.95)
       Predict: -0.8173343910336555
  Tree 27 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 1 <= 74.87)
      If (feature 1 <= 56.57)
       Predict: 0.28085003688072396
      Else (feature 1 > 56.57)
       Predict: -0.378551674966564
     Else (feature 1 > 74.87)
      If (feature 0 <= 21.42)
       Predict: -12.321588273833015
      Else (feature 0 > 21.42)
       Predict: 1.8659669412137414
    Else (feature 2 > 1028.38)
     If (feature 3 <= 89.83)
      If (feature 3 <= 66.27)
       Predict: -8.252928408643971
      Else (feature 3 > 66.27)
       Predict: -2.023910717088332
     Else (feature 3 > 89.83)
      If (feature 0 <= 8.39)
       Predict: -11.472893448110653
      Else (feature 0 > 8.39)
       Predict: -8.030312146910243
  Tree 28 (weight 0.1):
    If (feature 3 <= 85.4)
     If (feature 0 <= 7.55)
      If (feature 1 <= 40.05)
       Predict: 0.3456361310433187
      Else (feature 1 > 40.05)
       Predict: 4.958188742864418
     Else (feature 0 > 7.55)
      If (feature 0 <= 8.75)
       Predict: -3.0608059226719657
      Else (feature 0 > 8.75)
       Predict: 0.16507864507530287
    Else (feature 3 > 85.4)
     If (feature 2 <= 1015.63)
      If (feature 2 <= 1014.19)
       Predict: -0.3593841710339432
      Else (feature 2 > 1014.19)
       Predict: 3.2531365191458024
     Else (feature 2 > 1015.63)
      If (feature 1 <= 40.64)
       Predict: 1.0007657377910708
      Else (feature 1 > 40.64)
       Predict: -2.132339394694771
  Tree 29 (weight 0.1):
    If (feature 0 <= 30.56)
     If (feature 3 <= 55.74)
      If (feature 1 <= 72.24)
       Predict: 0.8569729911086951
      Else (feature 1 > 72.24)
       Predict: 6.358127096088517
     Else (feature 3 > 55.74)
      If (feature 1 <= 41.48)
       Predict: 0.43148253820326676
      Else (feature 1 > 41.48)
       Predict: -0.24352278568573174
    Else (feature 0 > 30.56)
     If (feature 2 <= 1014.35)
      If (feature 1 <= 68.3)
       Predict: -2.5522103291398683
      Else (feature 1 > 68.3)
       Predict: -0.21266182300917044
     Else (feature 2 > 1014.35)
      If (feature 1 <= 74.87)
       Predict: -6.498613011225412
      Else (feature 1 > 74.87)
       Predict: 0.9765776955731879
  Tree 30 (weight 0.1):
    If (feature 0 <= 17.84)
     If (feature 1 <= 45.08)
      If (feature 0 <= 15.33)
       Predict: -0.14424299831222268
      Else (feature 0 > 15.33)
       Predict: 1.8754751416891788
     Else (feature 1 > 45.08)
      If (feature 2 <= 1020.77)
       Predict: -3.097730832691005
      Else (feature 2 > 1020.77)
       Predict: -8.90070153022011
    Else (feature 0 > 17.84)
     If (feature 0 <= 18.71)
      If (feature 1 <= 49.02)
       Predict: 1.2726140970398088
      Else (feature 1 > 49.02)
       Predict: 6.649324687634596
     Else (feature 0 > 18.71)
      If (feature 1 <= 46.93)
       Predict: -2.818245204603037
      Else (feature 1 > 46.93)
       Predict: 0.23586447368304939
  Tree 31 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 59.14)
      If (feature 1 <= 50.66)
       Predict: -0.8733348655196066
      Else (feature 1 > 50.66)
       Predict: 7.928862441716025
     Else (feature 1 > 59.14)
      If (feature 1 <= 70.8)
       Predict: -3.8112988828197807
      Else (feature 1 > 70.8)
       Predict: 0.42812840935226704
    Else (feature 2 > 1004.52)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.07282772802501089
      Else (feature 1 > 46.93)
       Predict: -3.3364389464988706
     Else (feature 0 > 17.84)
      If (feature 2 <= 1020.32)
       Predict: 0.18419167853517965
      Else (feature 2 > 1020.32)
       Predict: 6.584432032190064
  Tree 32 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.39)
      If (feature 0 <= 13.56)
       Predict: 0.36741135502935035
      Else (feature 0 > 13.56)
       Predict: -0.7178818728654812
     Else (feature 1 > 49.39)
      If (feature 0 <= 17.84)
       Predict: -1.7883686826457996
      Else (feature 0 > 17.84)
       Predict: 4.519745157967235
    Else (feature 1 > 56.57)
     If (feature 0 <= 17.84)
      If (feature 0 <= 17.5)
       Predict: -4.182857837547887
      Else (feature 0 > 17.5)
       Predict: -7.917768935292194
     Else (feature 0 > 17.84)
      If (feature 0 <= 19.61)
       Predict: 2.6880627533068244
      Else (feature 0 > 19.61)
       Predict: -0.2998975340288976
  Tree 33 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 11.03)
      If (feature 3 <= 93.63)
       Predict: 0.7278554646891878
      Else (feature 3 > 93.63)
       Predict: -2.2492543009893162
     Else (feature 0 > 11.03)
      If (feature 2 <= 1024.3)
       Predict: -5.536706488618952
      Else (feature 2 > 1024.3)
       Predict: 4.479707018501001
    Else (feature 0 > 11.95)
     If (feature 0 <= 13.08)
      If (feature 0 <= 12.5)
       Predict: 5.173128471411881
      Else (feature 0 > 12.5)
       Predict: 2.3834255982190755
     Else (feature 0 > 13.08)
      If (feature 0 <= 15.33)
       Predict: -1.5022006203890645
      Else (feature 0 > 15.33)
       Predict: 0.15423852245074754
  Tree 34 (weight 0.1):
    If (feature 0 <= 8.75)
     If (feature 0 <= 7.55)
      If (feature 3 <= 77.56)
       Predict: 3.015852739381847
      Else (feature 3 > 77.56)
       Predict: -0.06103236076131486
     Else (feature 0 > 7.55)
      If (feature 3 <= 62.1)
       Predict: -13.594573386743992
      Else (feature 3 > 62.1)
       Predict: -2.6914920546129273
    Else (feature 0 > 8.75)
     If (feature 0 <= 10.03)
      If (feature 3 <= 95.45)
       Predict: 3.213047453934116
      Else (feature 3 > 95.45)
       Predict: -2.3699077010186502
     Else (feature 0 > 10.03)
      If (feature 0 <= 11.95)
       Predict: -1.841483689919706
      Else (feature 0 > 11.95)
       Predict: 0.1034719724734039
  Tree 35 (weight 0.1):
    If (feature 1 <= 56.57)
     If (feature 1 <= 49.02)
      If (feature 1 <= 44.88)
       Predict: 0.1854471597033813
      Else (feature 1 > 44.88)
       Predict: -1.537157071790549
     Else (feature 1 > 49.02)
      If (feature 2 <= 1009.77)
       Predict: -0.7176011396833722
      Else (feature 2 > 1009.77)
       Predict: 3.4414962844541495
    Else (feature 1 > 56.57)
     If (feature 1 <= 66.25)
      If (feature 0 <= 21.92)
       Predict: 0.6042503983890641
      Else (feature 0 > 21.92)
       Predict: -1.6430682984491796
     Else (feature 1 > 66.25)
      If (feature 0 <= 23.02)
       Predict: -3.919778656895867
      Else (feature 0 > 23.02)
       Predict: 0.8520833743461524
  Tree 36 (weight 0.1):
    If (feature 0 <= 27.6)
     If (feature 0 <= 23.02)
      If (feature 0 <= 22.1)
       Predict: 0.08610814822616036
      Else (feature 0 > 22.1)
       Predict: -3.39446668206219
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: -0.25067209339950686
      Else (feature 1 > 66.25)
       Predict: 2.1536703058787143
    Else (feature 0 > 27.6)
     If (feature 3 <= 62.1)
      If (feature 1 <= 74.87)
       Predict: -0.3912307208100507
      Else (feature 1 > 74.87)
       Predict: 2.6168301411252224
     Else (feature 3 > 62.1)
      If (feature 1 <= 71.8)
       Predict: -0.1075335658351684
      Else (feature 1 > 71.8)
       Predict: -3.3756176659678685
  Tree 37 (weight 0.1):
    If (feature 0 <= 25.35)
     If (feature 0 <= 23.02)
      If (feature 1 <= 64.84)
       Predict: 0.07789630965601392
      Else (feature 1 > 64.84)
       Predict: -2.8928836560033093
     Else (feature 0 > 23.02)
      If (feature 1 <= 66.25)
       Predict: 0.13731068060749954
      Else (feature 1 > 66.25)
       Predict: 4.15851454889221
    Else (feature 0 > 25.35)
     If (feature 1 <= 43.65)
      If (feature 0 <= 27.19)
       Predict: -16.475158304770883
      Else (feature 0 > 27.19)
       Predict: -7.947134756554647
     Else (feature 1 > 43.65)
      If (feature 3 <= 62.7)
       Predict: 0.1725950049938879
      Else (feature 3 > 62.7)
       Predict: -1.0926147971432427
  Tree 38 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 0 <= 30.56)
      If (feature 3 <= 47.89)
       Predict: 1.6647926733523803
      Else (feature 3 > 47.89)
       Predict: 0.019004190066623235
     Else (feature 0 > 30.56)
      If (feature 2 <= 1014.35)
       Predict: -0.6192794789083232
      Else (feature 2 > 1014.35)
       Predict: -4.385760311827676
    Else (feature 2 > 1028.38)
     If (feature 1 <= 39.48)
      If (feature 0 <= 6.52)
       Predict: 4.573467616169609
      Else (feature 0 > 6.52)
       Predict: -1.362091279334777
     Else (feature 1 > 39.48)
      If (feature 0 <= 8.75)
       Predict: -7.0007999537928605
      Else (feature 0 > 8.75)
       Predict: -1.617908469279585
  Tree 39 (weight 0.1):
    If (feature 2 <= 1017.42)
     If (feature 2 <= 1014.19)
      If (feature 1 <= 43.13)
       Predict: 1.2098492492388833
      Else (feature 1 > 43.13)
       Predict: -0.4345828650352739
     Else (feature 2 > 1014.19)
      If (feature 3 <= 96.38)
       Predict: 1.0830640036331665
      Else (feature 3 > 96.38)
       Predict: -6.6054777318343785
    Else (feature 2 > 1017.42)
     If (feature 2 <= 1019.23)
      If (feature 1 <= 57.85)
       Predict: -0.8212874032064794
      Else (feature 1 > 57.85)
       Predict: -2.6667829000634105
     Else (feature 2 > 1019.23)
      If (feature 0 <= 17.84)
       Predict: -0.39094381687835245
      Else (feature 0 > 17.84)
       Predict: 3.336117383932137
  Tree 40 (weight 0.1):
    If (feature 3 <= 75.23)
     If (feature 1 <= 40.05)
      If (feature 1 <= 39.96)
       Predict: -1.2851367407493581
      Else (feature 1 > 39.96)
       Predict: -9.117459296991676
     Else (feature 1 > 40.05)
      If (feature 1 <= 40.89)
       Predict: 4.461974679211411
      Else (feature 1 > 40.89)
       Predict: 0.25422282080546216
    Else (feature 3 > 75.23)
     If (feature 0 <= 21.42)
      If (feature 0 <= 17.84)
       Predict: -0.11457026696795661
      Else (feature 0 > 17.84)
       Predict: 0.9995406591682215
     Else (feature 0 > 21.42)
      If (feature 0 <= 23.02)
       Predict: -2.664637163988949
      Else (feature 0 > 23.02)
       Predict: -0.5023743568762508
  Tree 41 (weight 0.1):
    If (feature 2 <= 1001.9)
     If (feature 1 <= 39.13)
      If (feature 3 <= 79.95)
       Predict: 9.0188365708008
      Else (feature 3 > 79.95)
       Predict: 2.9702965803786205
     Else (feature 1 > 39.13)
      If (feature 3 <= 63.68)
       Predict: -4.052067945951171
      Else (feature 3 > 63.68)
       Predict: -1.0796516186664176
    Else (feature 2 > 1001.9)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.38)
       Predict: 0.15316006561614587
      Else (feature 0 > 14.38)
       Predict: -3.487291240038168
     Else (feature 0 > 15.33)
      If (feature 1 <= 43.13)
       Predict: 2.5605988792505605
      Else (feature 1 > 43.13)
       Predict: 0.03166127813460667
  Tree 42 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 11.42)
      If (feature 1 <= 38.25)
       Predict: -2.0532785635493065
      Else (feature 1 > 38.25)
       Predict: 0.4665697970110133
     Else (feature 0 > 11.42)
      If (feature 1 <= 44.2)
       Predict: -4.178641719198364
      Else (feature 1 > 44.2)
       Predict: -9.84024023297988
    Else (feature 0 > 11.95)
     If (feature 0 <= 13.08)
      If (feature 1 <= 40.89)
       Predict: 4.383821312183712
      Else (feature 1 > 40.89)
       Predict: 2.000819554066434
     Else (feature 0 > 13.08)
      If (feature 0 <= 15.33)
       Predict: -1.0813581518144955
      Else (feature 0 > 15.33)
       Predict: 0.11492139312962121
  Tree 43 (weight 0.1):
    If (feature 0 <= 8.75)
     If (feature 0 <= 7.97)
      If (feature 3 <= 86.54)
       Predict: 0.983392336251922
      Else (feature 3 > 86.54)
       Predict: -0.8690504742953818
     Else (feature 0 > 7.97)
      If (feature 3 <= 62.1)
       Predict: -20.310342278835464
      Else (feature 3 > 62.1)
       Predict: -2.975869736741497
    Else (feature 0 > 8.75)
     If (feature 0 <= 9.42)
      If (feature 2 <= 1015.45)
       Predict: 5.74314556767472
      Else (feature 2 > 1015.45)
       Predict: 2.1033141679659995
     Else (feature 0 > 9.42)
      If (feature 1 <= 40.89)
       Predict: 0.6933339562649613
      Else (feature 1 > 40.89)
       Predict: -0.10718368674776323
  Tree 44 (weight 0.1):
    If (feature 1 <= 74.87)
     If (feature 1 <= 71.43)
      If (feature 1 <= 68.3)
       Predict: -0.0751396787352361
      Else (feature 1 > 68.3)
       Predict: 1.0387569941322914
     Else (feature 1 > 71.43)
      If (feature 1 <= 72.86)
       Predict: -2.5461711201599986
      Else (feature 1 > 72.86)
       Predict: -0.0018936704520639966
    Else (feature 1 > 74.87)
     If (feature 1 <= 77.3)
      If (feature 3 <= 73.33)
       Predict: 3.4362919081871732
      Else (feature 3 > 73.33)
       Predict: 0.022595797531833054
     Else (feature 1 > 77.3)
      If (feature 2 <= 1012.39)
       Predict: -2.0026738842740444
      Else (feature 2 > 1012.39)
       Predict: 1.7553499174736846
  Tree 45 (weight 0.1):
    If (feature 2 <= 1005.35)
     If (feature 1 <= 72.24)
      If (feature 1 <= 59.14)
       Predict: 0.030127466104975898
      Else (feature 1 > 59.14)
       Predict: -2.2341894812350676
     Else (feature 1 > 72.24)
      If (feature 3 <= 60.09)
       Predict: 4.41863108135717
      Else (feature 3 > 60.09)
       Predict: -0.11040726869235623
    Else (feature 2 > 1005.35)
     If (feature 0 <= 31.8)
      If (feature 1 <= 66.25)
       Predict: -0.06640264597455495
      Else (feature 1 > 66.25)
       Predict: 0.6711276381424462
     Else (feature 0 > 31.8)
      If (feature 1 <= 62.44)
       Predict: 18.071299971628946
      Else (feature 1 > 62.44)
       Predict: -1.613111097205577
  Tree 46 (weight 0.1):
    If (feature 0 <= 25.95)
     If (feature 0 <= 23.02)
      If (feature 0 <= 22.6)
       Predict: 0.0037802976144726266
      Else (feature 0 > 22.6)
       Predict: -3.2702083989998565
     Else (feature 0 > 23.02)
      If (feature 1 <= 47.83)
       Predict: 7.351532379664369
      Else (feature 1 > 47.83)
       Predict: 0.6617643737173495
    Else (feature 0 > 25.95)
     If (feature 3 <= 62.1)
      If (feature 0 <= 29.89)
       Predict: 0.7522949567047181
      Else (feature 0 > 29.89)
       Predict: -0.5659530686126862
     Else (feature 3 > 62.1)
      If (feature 1 <= 43.41)
       Predict: -9.179671352130104
      Else (feature 1 > 43.41)
       Predict: -0.9646184420761758
  Tree 47 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 38.62)
      If (feature 3 <= 77.17)
       Predict: -4.215696425771664
      Else (feature 3 > 77.17)
       Predict: 5.655069692148392
     Else (feature 1 > 38.62)
      If (feature 1 <= 39.13)
       Predict: -12.269101167501105
      Else (feature 1 > 39.13)
       Predict: 1.081763483601667
    Else (feature 0 > 5.18)
     If (feature 0 <= 8.75)
      If (feature 0 <= 7.97)
       Predict: -0.19756946285599916
      Else (feature 0 > 7.97)
       Predict: -2.7184931590940438
     Else (feature 0 > 8.75)
      If (feature 0 <= 9.42)
       Predict: 2.558566383813981
      Else (feature 0 > 9.42)
       Predict: -0.006722635545763743
  Tree 48 (weight 0.1):
    If (feature 2 <= 1028.38)
     If (feature 2 <= 1010.89)
      If (feature 1 <= 66.93)
       Predict: -0.7473456438858288
      Else (feature 1 > 66.93)
       Predict: 0.34762458916260297
     Else (feature 2 > 1010.89)
      If (feature 1 <= 58.86)
       Predict: 0.4001213596367478
      Else (feature 1 > 58.86)
       Predict: -0.33373941983121597
    Else (feature 2 > 1028.38)
     If (feature 1 <= 42.85)
      If (feature 1 <= 39.48)
       Predict: 2.1904388134214514
      Else (feature 1 > 39.48)
       Predict: -3.2474441160938956
     Else (feature 1 > 42.85)
      If (feature 3 <= 71.55)
       Predict: -1.061140549595708
      Else (feature 3 > 71.55)
       Predict: 6.934556118848832
  Tree 49 (weight 0.1):
    If (feature 0 <= 11.95)
     If (feature 0 <= 10.74)
      If (feature 0 <= 8.75)
       Predict: -0.48190999213172564
      Else (feature 0 > 8.75)
       Predict: 1.0350335598803566
     Else (feature 0 > 10.74)
      If (feature 2 <= 1024.3)
       Predict: -3.057989388513731
      Else (feature 2 > 1024.3)
       Predict: 2.162024696272738
    Else (feature 0 > 11.95)
     If (feature 0 <= 12.5)
      If (feature 3 <= 86.91)
       Predict: 4.627051067913808
      Else (feature 3 > 86.91)
       Predict: 0.9386052167341327
     Else (feature 0 > 12.5)
      If (feature 1 <= 37.8)
       Predict: 4.0889321278523685
      Else (feature 1 > 37.8)
       Predict: -0.02245818963891235
  Tree 50 (weight 0.1):
    If (feature 2 <= 1017.42)
     If (feature 2 <= 1014.19)
      If (feature 1 <= 43.13)
       Predict: 0.9320375696962719
      Else (feature 1 > 43.13)
       Predict: -0.31844348507047093
     Else (feature 2 > 1014.19)
      If (feature 1 <= 42.42)
       Predict: -0.5988031510673222
      Else (feature 1 > 42.42)
       Predict: 1.3187243855742212
    Else (feature 2 > 1017.42)
     If (feature 2 <= 1019.23)
      If (feature 1 <= 44.2)
       Predict: -2.0646082455368195
      Else (feature 1 > 44.2)
       Predict: -0.4969601265683861
     Else (feature 2 > 1019.23)
      If (feature 0 <= 17.84)
       Predict: -0.2870181057370213
      Else (feature 0 > 17.84)
       Predict: 2.6148230736448608
  Tree 51 (weight 0.1):
    If (feature 1 <= 38.62)
     If (feature 0 <= 18.4)
      If (feature 0 <= 5.18)
       Predict: 3.850885339006515
      Else (feature 0 > 5.18)
       Predict: -0.940687510645146
     Else (feature 0 > 18.4)
      If (feature 0 <= 18.98)
       Predict: -10.80330040562501
      Else (feature 0 > 18.98)
       Predict: -18.03404880535599
    Else (feature 1 > 38.62)
     If (feature 2 <= 1026.23)
      If (feature 0 <= 13.56)
       Predict: 0.5295719576334972
      Else (feature 0 > 13.56)
       Predict: -0.052812717813551166
     Else (feature 2 > 1026.23)
      If (feature 1 <= 40.22)
       Predict: -4.371246083031292
      Else (feature 1 > 40.22)
       Predict: -1.3541229527292618
  Tree 52 (weight 0.1):
    If (feature 1 <= 66.25)
     If (feature 1 <= 64.84)
      If (feature 3 <= 41.26)
       Predict: 3.045631536773922
      Else (feature 3 > 41.26)
       Predict: -0.0337837562463145
     Else (feature 1 > 64.84)
      If (feature 1 <= 65.27)
       Predict: -5.921444872611693
      Else (feature 1 > 65.27)
       Predict: -0.8270282146869598
    Else (feature 1 > 66.25)
     If (feature 0 <= 23.02)
      If (feature 0 <= 19.83)
       Predict: 1.5405239234096135
      Else (feature 0 > 19.83)
       Predict: -3.1288830506195398
     Else (feature 0 > 23.02)
      If (feature 0 <= 25.35)
       Predict: 3.2672442442602656
      Else (feature 0 > 25.35)
       Predict: -0.007592990267182966
  Tree 53 (weight 0.1):
    If (feature 0 <= 17.84)
     If (feature 1 <= 46.93)
      If (feature 0 <= 17.2)
       Predict: 0.1228349542857993
      Else (feature 0 > 17.2)
       Predict: -2.392588492043597
     Else (feature 1 > 46.93)
      If (feature 2 <= 1020.77)
       Predict: -1.8240349072310669
      Else (feature 2 > 1020.77)
       Predict: -6.523289398433308
    Else (feature 0 > 17.84)
     If (feature 0 <= 18.4)
      If (feature 1 <= 47.83)
       Predict: 0.5318997435908227
      Else (feature 1 > 47.83)
       Predict: 4.907584149653537
     Else (feature 0 > 18.4)
      If (feature 1 <= 46.93)
       Predict: -2.110133253015907
      Else (feature 1 > 46.93)
       Predict: 0.20708863671712482
  Tree 54 (weight 0.1):
    If (feature 3 <= 76.79)
     If (feature 1 <= 40.05)
      If (feature 1 <= 39.96)
       Predict: -0.7416033424896232
      Else (feature 1 > 39.96)
       Predict: -6.880323474190146
     Else (feature 1 > 40.05)
      If (feature 1 <= 40.89)
       Predict: 2.887497917363201
      Else (feature 1 > 40.89)
       Predict: 0.17777582956662522
    Else (feature 3 > 76.79)
     If (feature 0 <= 19.61)
      If (feature 0 <= 17.84)
       Predict: -0.09172434324104897
      Else (feature 0 > 17.84)
       Predict: 1.9482862934683598
     Else (feature 0 > 19.61)
      If (feature 2 <= 1010.6)
       Predict: -0.15262790703036064
      Else (feature 2 > 1010.6)
       Predict: -1.7280878096087295
  Tree 55 (weight 0.1):
    If (feature 0 <= 24.79)
     If (feature 0 <= 23.02)
      If (feature 1 <= 66.93)
       Predict: 0.02682576814507517
      Else (feature 1 > 66.93)
       Predict: -2.323863726560255
     Else (feature 0 > 23.02)
      If (feature 1 <= 47.83)
       Predict: 6.909290893058579
      Else (feature 1 > 47.83)
       Predict: 0.9944889736997976
    Else (feature 0 > 24.79)
     If (feature 3 <= 65.24)
      If (feature 0 <= 28.5)
       Predict: 0.8432916332803679
      Else (feature 0 > 28.5)
       Predict: -0.3680864130080106
     Else (feature 3 > 65.24)
      If (feature 1 <= 66.51)
       Predict: -2.1147474860288
      Else (feature 1 > 66.51)
       Predict: -0.3834883036951788
  Tree 56 (weight 0.1):
    If (feature 0 <= 15.33)
     If (feature 0 <= 14.38)
      If (feature 0 <= 11.95)
       Predict: -0.3290262091199092
      Else (feature 0 > 11.95)
       Predict: 0.8543511625463592
     Else (feature 0 > 14.38)
      If (feature 2 <= 1016.21)
       Predict: -0.7208476709379852
      Else (feature 2 > 1016.21)
       Predict: -4.40928839539672
    Else (feature 0 > 15.33)
     If (feature 0 <= 16.22)
      If (feature 2 <= 1013.19)
       Predict: 4.554268903891635
      Else (feature 2 > 1013.19)
       Predict: 1.538781048856137
     Else (feature 0 > 16.22)
      If (feature 1 <= 46.93)
       Predict: -1.1488437756174756
      Else (feature 1 > 46.93)
       Predict: 0.1634274865006602
  Tree 57 (weight 0.1):
    If (feature 2 <= 1007.46)
     If (feature 1 <= 73.67)
      If (feature 1 <= 71.43)
       Predict: -0.28457458674767294
      Else (feature 1 > 71.43)
       Predict: -2.556284198496123
     Else (feature 1 > 73.67)
      If (feature 3 <= 60.81)
       Predict: 4.31886476056719
      Else (feature 3 > 60.81)
       Predict: 0.3197495651743129
    Else (feature 2 > 1007.46)
     If (feature 0 <= 17.84)
      If (feature 1 <= 46.93)
       Predict: 0.04575453109929229
      Else (feature 1 > 46.93)
       Predict: -2.141138284310683
     Else (feature 0 > 17.84)
      If (feature 1 <= 56.57)
       Predict: 1.3439965861050847
      Else (feature 1 > 56.57)
       Predict: -0.02904919315788331
  Tree 58 (weight 0.1):
    If (feature 0 <= 31.8)
     If (feature 1 <= 66.25)
      If (feature 1 <= 64.84)
       Predict: -0.006836636445003446
      Else (feature 1 > 64.84)
       Predict: -2.0890363043188134
     Else (feature 1 > 66.25)
      If (feature 1 <= 69.05)
       Predict: 1.8596834938858298
      Else (feature 1 > 69.05)
       Predict: -0.2637818907162569
    Else (feature 0 > 31.8)
     If (feature 1 <= 69.34)
      If (feature 2 <= 1009.63)
       Predict: -4.53407923927751
      Else (feature 2 > 1009.63)
       Predict: 1.2479530412848983
     Else (feature 1 > 69.34)
      If (feature 1 <= 69.88)
       Predict: 5.672382101944148
      Else (feature 1 > 69.88)
       Predict: -0.7728960613425813
  Tree 59 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 68.3)
      If (feature 1 <= 43.41)
       Predict: 0.423961936091299
      Else (feature 1 > 43.41)
       Predict: -1.0411314850417004
     Else (feature 1 > 68.3)
      If (feature 1 <= 68.67)
       Predict: 7.130757445704555
      Else (feature 1 > 68.67)
       Predict: 0.1160942217864609
    Else (feature 2 > 1010.89)
     If (feature 3 <= 93.63)
      If (feature 1 <= 58.86)
       Predict: 0.41091291246834866
      Else (feature 1 > 58.86)
       Predict: -0.2764637915143923
     Else (feature 3 > 93.63)
      If (feature 1 <= 41.74)
       Predict: -3.564757715833512
      Else (feature 1 > 41.74)
       Predict: 1.1644353912440248
  Tree 60 (weight 0.1):
    If (feature 1 <= 48.6)
     If (feature 1 <= 44.88)
      If (feature 2 <= 1016.57)
       Predict: 0.4410572983039277
      Else (feature 2 > 1016.57)
       Predict: -0.44414793681792664
     Else (feature 1 > 44.88)
      If (feature 2 <= 1014.35)
       Predict: -3.0626378082153085
      Else (feature 2 > 1014.35)
       Predict: 2.0328536525605063
    Else (feature 1 > 48.6)
     If (feature 1 <= 52.05)
      If (feature 2 <= 1009.9)
       Predict: 0.24004783900051171
      Else (feature 2 > 1009.9)
       Predict: 3.1645061792332916
     Else (feature 1 > 52.05)
      If (feature 0 <= 17.84)
       Predict: -1.95074879327582
      Else (feature 0 > 17.84)
       Predict: 0.021106826304965107
  Tree 61 (weight 0.1):
    If (feature 1 <= 74.87)
     If (feature 1 <= 71.43)
      If (feature 1 <= 68.3)
       Predict: -0.06241270845694165
      Else (feature 1 > 68.3)
       Predict: 0.8051320337219834
     Else (feature 1 > 71.43)
      If (feature 0 <= 24.57)
       Predict: 1.648459594873699
      Else (feature 0 > 24.57)
       Predict: -1.2314608832462137
    Else (feature 1 > 74.87)
     If (feature 1 <= 77.3)
      If (feature 0 <= 21.42)
       Predict: -7.482222216002697
      Else (feature 0 > 21.42)
       Predict: 1.8228183337802573
     Else (feature 1 > 77.3)
      If (feature 2 <= 1012.39)
       Predict: -1.4326641812285505
      Else (feature 2 > 1012.39)
       Predict: 1.7079353624089986
  Tree 62 (weight 0.1):
    If (feature 0 <= 5.18)
     If (feature 1 <= 42.07)
      If (feature 3 <= 96.38)
       Predict: 1.4583097259406885
      Else (feature 3 > 96.38)
       Predict: 7.4053761713858615
     Else (feature 1 > 42.07)
      If (feature 2 <= 1008.19)
       Predict: 0.311290850436914
      Else (feature 2 > 1008.19)
       Predict: -5.145119802972147
    Else (feature 0 > 5.18)
     If (feature 1 <= 38.62)
      If (feature 0 <= 18.4)
       Predict: -0.7259884411546618
      Else (feature 0 > 18.4)
       Predict: -12.427884135864616
     Else (feature 1 > 38.62)
      If (feature 1 <= 39.48)
       Predict: 1.131291291234381
      Else (feature 1 > 39.48)
       Predict: -0.007004055574359982
  Tree 63 (weight 0.1):
    If (feature 2 <= 1004.52)
     If (feature 1 <= 70.8)
      If (feature 1 <= 69.05)
       Predict: -0.45566718124370104
      Else (feature 1 > 69.05)
       Predict: -3.3633539333883373
     Else (feature 1 > 70.8)
      If (feature 3 <= 70.63)
       Predict: 1.7061073842258219
      Else (feature 3 > 70.63)
       Predict: -0.35469491259927843
    Else (feature 2 > 1004.52)
     If (feature 0 <= 15.33)
      If (feature 0 <= 14.13)
       Predict: 0.13165022513417465
      Else (feature 0 > 14.13)
       Predict: -1.8886218519887454
     Else (feature 0 > 15.33)
      If (feature 1 <= 43.13)
       Predict: 2.0897911694212086
      Else (feature 1 > 43.13)
       Predict: 0.023571622513158218
  Tree 64 (weight 0.1):
    If (feature 1 <= 41.92)
     If (feature 1 <= 41.58)
      If (feature 2 <= 1015.45)
       Predict: 0.6420804366913081
      Else (feature 2 > 1015.45)
       Predict: -0.3393001000428116
     Else (feature 1 > 41.58)
      If (feature 3 <= 91.38)
       Predict: -2.959889489145066
      Else (feature 3 > 91.38)
       Predict: -14.822621379271645
    Else (feature 1 > 41.92)
     If (feature 1 <= 43.13)
      If (feature 0 <= 15.33)
       Predict: 0.5584851317693598
      Else (feature 0 > 15.33)
       Predict: 5.35806974907062
     Else (feature 1 > 43.13)
      If (feature 1 <= 43.65)
       Predict: -2.5734171913252673
      Else (feature 1 > 43.65)
       Predict: 0.06206747847844893
  Tree 65 (weight 0.1):
    If (feature 2 <= 1010.89)
     If (feature 1 <= 66.93)
      If (feature 0 <= 20.6)
       Predict: -0.0679333275254979
      Else (feature 0 > 20.6)
       Predict: -1.053808811058633
     Else (feature 1 > 66.93)
      If (feature 1 <= 67.32)
       Predict: 7.372080266725638
      Else (feature 1 > 67.32)
       Predict: 0.09996335027123535
    Else (feature 2 > 1010.89)
     If (feature 3 <= 75.61)
      If (feature 1 <= 40.05)
       Predict: -0.9831581524231143
      Else (feature 1 > 40.05)
       Predict: 0.5486160789249349
     Else (feature 3 > 75.61)
      If (feature 1 <= 58.86)
       Predict: 0.19399224442246701
      Else (feature 1 > 58.86)
       Predict: -1.5652059699408227
  Tree 66 (weight 0.1):
    If (feature 0 <= 28.75)
     If (feature 1 <= 73.18)
      If (feature 1 <= 71.43)
       Predict: 0.05143978594106816
      Else (feature 1 > 71.43)
       Predict: -1.436513600322334
     Else (feature 1 > 73.18)
      If (feature 3 <= 73.33)
       Predict: 4.1459864582084975
      Else (feature 3 > 73.33)
       Predict: 0.34965185037807356
    Else (feature 0 > 28.75)
     If (feature 2 <= 1014.54)
      If (feature 2 <= 1013.43)
       Predict: -0.4008005884834272
      Else (feature 2 > 1013.43)
       Predict: 3.683818693727259
     Else (feature 2 > 1014.54)
      If (feature 1 <= 67.83)
       Predict: -0.82614879352537
      Else (feature 1 > 67.83)
       Predict: -4.535981326886069
  Tree 67 (weight 0.1):
    If (feature 1 <= 47.83)
     If (feature 0 <= 23.02)
      If (feature 0 <= 18.71)
       Predict: -0.0010074123242523121
      Else (feature 0 > 18.71)
       Predict: -3.2926535011699234
     Else (feature 0 > 23.02)
      If (feature 2 <= 1012.39)
       Predict: 1.3034696914565052
      Else (feature 2 > 1012.39)
       Predict: 11.235282784300427
    Else (feature 1 > 47.83)
     If (feature 1 <= 56.57)
      If (feature 0 <= 17.84)
       Predict: -1.039931035628621
      Else (feature 0 > 17.84)
       Predict: 1.9905896386111916
     Else (feature 1 > 56.57)
      If (feature 1 <= 57.19)
       Predict: -2.3357601760278204
      Else (feature 1 > 57.19)
       Predict: -0.0355403353056693
  Tree 68 (weight 0.1):
    If (feature 0 <= 24.79)
     If (feature 3 <= 41.26)
      If (feature 1 <= 45.87)
       Predict: 2.4904273637383265
      Else (feature 1 > 45.87)
       Predict: 13.013875696314063
     Else (feature 3 > 41.26)
      If (feature 1 <= 49.02)
       Predict: -0.18642415027276396
      Else (feature 1 > 49.02)
       Predict: 0.47121076166963227
    Else (feature 0 > 24.79)
     If (feature 1 <= 65.27)
      If (feature 1 <= 64.84)
       Predict: -0.5...

Step 8: Deployment

Now that we have a predictive model it is time to deploy the model into an operational environment.

In our example, let's say we have a series of sensors attached to the power plant and a monitoring station.

The monitoring station will need close to real-time information about how much power that their station will generate so they can relay that to the utility.

So let's create a Spark Streaming utility that we can use for this purpose.

See http://spark.apache.org/docs/latest/streaming-programming-guide.html if you can't wait!

After deployment you will be able to use the best predictions from gradient boosed regression trees to feed a real-time dashboard or feed the utility with information on how much power the peaker plant will deliver give current conditions.

// Let's set the variable finalModel to our best GBT Model
val finalModel = gbtModel.bestModel

finalModel: org.apache.spark.ml.Model[_] = pipeline_e6a84d2d75ba

//gbtModel.bestModel.asInstanceOf[PipelineModel]//.stages.last.asInstanceOf[GBTRegressionModel]
//        .write.overwrite().save("dbfs:///databricks/driver/MyTrainedGbtPipelineModel")

//val finalModel = PipelineModel.load("dbfs:///databricks/driver/MyTrainedGbtPipelineModel/")

Let's create our table for predictions

DROP TABLE IF EXISTS power_plant_predictions ;
CREATE TABLE power_plant_predictions(
  AT Double,
  V Double,
  AP Double,
  RH Double,
  PE Double,
  Predicted_PE Double
);

This should be updated to structured streaming - after the break.

Now let's create our streaming job to score new power plant readings in real-time.

CAUTION: There can be only one spark streaming context per cluster!!! So please check if a streaming context is already alive first.

import java.nio.ByteBuffer
import java.net._
import java.io._
import concurrent._
import scala.io._
import sys.process._
//import org.apache.spark.Logging
import org.apache.spark.SparkConf
import org.apache.spark.storage.StorageLevel
import org.apache.spark.streaming.Seconds
import org.apache.spark.streaming.Minutes
import org.apache.spark.streaming.StreamingContext
//import org.apache.spark.streaming.StreamingContext.toPairDStreamFunctions
import org.apache.log4j.Logger
import org.apache.log4j.Level
import org.apache.spark.streaming.receiver.Receiver
import sqlContext._
import net.liftweb.json.DefaultFormats
import net.liftweb.json._

import scala.collection.mutable.SynchronizedQueue


val queue = new SynchronizedQueue[RDD[String]]()

val batchIntervalSeconds = 2

var newContextCreated = false      // Flag to detect whether new context was created or not

// Function to create a new StreamingContext and set it up
def creatingFunc(): StreamingContext = {

  // Create a StreamingContext
  val ssc = new StreamingContext(sc, Seconds(batchIntervalSeconds))
  val batchInterval = Seconds(1)
  ssc.remember(Seconds(300))
  val dstream = ssc.queueStream(queue)
  dstream.foreachRDD { 
    rdd =>
      // if the RDD has data
       if(!(rdd.isEmpty())) {
          // Use the final model to transform a JSON message into a dataframe and pass the dataframe to our model's transform method
           finalModel
             .transform(read.json(rdd.toDS).toDF())
         // Select only columns we are interested in
         .select("AT", "V", "AP", "RH", "PE", "Predicted_PE")
         // Append the results to our power_plant_predictions table
         .write.mode(SaveMode.Append).format("hive").saveAsTable("power_plant_predictions")
       } 
  }
  println("Creating function called to create new StreamingContext for Power Plant Predictions")
  newContextCreated = true  
  ssc
}

val ssc = StreamingContext.getActiveOrCreate(creatingFunc)
if (newContextCreated) {
  println("New context created from currently defined creating function") 
} else {
  println("Existing context running or recovered from checkpoint, may not be running currently defined creating function")
}

ssc.start()

Creating function called to create new StreamingContext for Power Plant Predictions
New context created from currently defined creating function
<console>:303: warning: class SynchronizedQueue in package mutable is deprecated: Synchronization via selective overriding of methods is inherently unreliable.  Consider java.util.concurrent.ConcurrentLinkedQueue as an alternative.
       val queue = new SynchronizedQueue[RDD[String]]()
                       ^
import java.nio.ByteBuffer
import java.net._
import java.io._
import concurrent._
import scala.io._
import sys.process._
import org.apache.spark.SparkConf
import org.apache.spark.storage.StorageLevel
import org.apache.spark.streaming.Seconds
import org.apache.spark.streaming.Minutes
import org.apache.spark.streaming.StreamingContext
import org.apache.log4j.Logger
import org.apache.log4j.Level
import org.apache.spark.streaming.receiver.Receiver
import sqlContext._
import net.liftweb.json.DefaultFormats
import net.liftweb.json._
import scala.collection.mutable.SynchronizedQueue
queue: scala.collection.mutable.SynchronizedQueue[org.apache.spark.rdd.RDD[String]] = SynchronizedQueue()
batchIntervalSeconds: Int = 2
newContextCreated: Boolean = true
creatingFunc: ()org.apache.spark.streaming.StreamingContext
ssc: org.apache.spark.streaming.StreamingContext = org.apache.spark.streaming.StreamingContext@4a48de26

Now that we have created and defined our streaming job, let's test it with some data. First we clear the predictions table.

truncate table power_plant_predictions

Let's use data to see how much power output our model will predict.

// First we try it with a record from our test set and see what we get:
queue += sc.makeRDD(Seq(s"""{"AT":10.82,"V":37.5,"AP":1009.23,"RH":96.62,"PE":473.9}"""))

// We may need to wait a few seconds for data to appear in the table
Thread.sleep(Seconds(5).milliseconds)

--and we can query our predictions table
select * from power_plant_predictions

Let's repeat with a different test measurement that our model has not seen before:

queue += sc.makeRDD(Seq(s"""{"AT":10.0,"V":40,"AP":1000,"RH":90.0,"PE":0.0}"""))
Thread.sleep(Seconds(5).milliseconds)

--Note you may have to run this a couple of times to see the refreshed data...
select * from power_plant_predictions

As you can see the Predictions are very close to the real data points.

select * from power_plant_table where AT between 10 and 11 and AP between 1000 and 1010 and RH between 90 and 97 and v between 37 and 40 order by PE

Now you use the predictions table to feed a real-time dashboard or feed the utility with information on how much power the peaker plant will deliver.

Make sure the streaming context is stopped when you are done, as there can be only one such context per cluster!

ssc.stop(stopSparkContext = false) // gotto stop or it ill keep running!!!

Datasource References:

• Pinar Tüfekci, Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods, International Journal of Electrical Power & Energy Systems, Volume 60, September 2014, Pages 126-140, ISSN 0142-0615, Web Link
• Heysem Kaya, Pinar Tüfekci , Sadik Fikret Gürgen: Local and Global Learning Methods for Predicting Power of a Combined Gas & Steam Turbine, Proceedings of the International Conference on Emerging Trends in Computer and Electronics Engineering ICETCEE 2012, pp. 13-18 (Mar. 2012, Dubai) Web Link