[SPARK-9005] [MLLIB] Fix RegressionMetrics computation of explainedVariance
Fixes implementation of `explainedVariance` and `r2` to be consistent with their definitions as described in [SPARK-9005](https://issues.apache.org/jira/browse/SPARK-9005). Author: Feynman Liang <fliang@databricks.com> Closes #7361 from feynmanliang/SPARK-9005-RegressionMetrics-bugs and squashes the following commits: f1112fc [Feynman Liang] Add explainedVariance formula 1a3d098 [Feynman Liang] SROwen code review comments 08a0e1b [Feynman Liang] Fix pyspark tests db8605a [Feynman Liang] Style fix bde9761 [Feynman Liang] Fix RegressionMetrics tests, relax assumption predictor is unbiased c235de0 [Feynman Liang] Fix RegressionMetrics tests 4c4e56f [Feynman Liang] Fix RegressionMetrics computation of explainedVariance and r2
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@ -53,14 +53,22 @@ class RegressionMetrics(predictionAndObservations: RDD[(Double, Double)]) extend
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)
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summary
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}
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private lazy val SSerr = math.pow(summary.normL2(1), 2)
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private lazy val SStot = summary.variance(0) * (summary.count - 1)
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private lazy val SSreg = {
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val yMean = summary.mean(0)
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predictionAndObservations.map {
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case (prediction, _) => math.pow(prediction - yMean, 2)
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}.sum()
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}
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/**
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* Returns the explained variance regression score.
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* explainedVariance = 1 - variance(y - \hat{y}) / variance(y)
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* Reference: [[http://en.wikipedia.org/wiki/Explained_variation]]
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* Returns the variance explained by regression.
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* explainedVariance = \sum_i (\hat{y_i} - \bar{y})^2 / n
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* @see [[https://en.wikipedia.org/wiki/Fraction_of_variance_unexplained]]
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*/
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def explainedVariance: Double = {
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1 - summary.variance(1) / summary.variance(0)
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SSreg / summary.count
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}
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/**
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@ -76,8 +84,7 @@ class RegressionMetrics(predictionAndObservations: RDD[(Double, Double)]) extend
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* expected value of the squared error loss or quadratic loss.
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*/
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def meanSquaredError: Double = {
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val rmse = summary.normL2(1) / math.sqrt(summary.count)
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rmse * rmse
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SSerr / summary.count
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}
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/**
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@ -85,14 +92,14 @@ class RegressionMetrics(predictionAndObservations: RDD[(Double, Double)]) extend
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* the mean squared error.
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*/
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def rootMeanSquaredError: Double = {
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summary.normL2(1) / math.sqrt(summary.count)
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math.sqrt(this.meanSquaredError)
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}
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/**
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* Returns R^2^, the coefficient of determination.
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* Reference: [[http://en.wikipedia.org/wiki/Coefficient_of_determination]]
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* Returns R^2^, the unadjusted coefficient of determination.
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* @see [[http://en.wikipedia.org/wiki/Coefficient_of_determination]]
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*/
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def r2: Double = {
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1 - math.pow(summary.normL2(1), 2) / (summary.variance(0) * (summary.count - 1))
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1 - SSerr / SStot
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}
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}
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@ -23,24 +23,85 @@ import org.apache.spark.mllib.util.TestingUtils._
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class RegressionMetricsSuite extends SparkFunSuite with MLlibTestSparkContext {
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test("regression metrics") {
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test("regression metrics for unbiased (includes intercept term) predictor") {
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/* Verify results in R:
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preds = c(2.25, -0.25, 1.75, 7.75)
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obs = c(3.0, -0.5, 2.0, 7.0)
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SStot = sum((obs - mean(obs))^2)
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SSreg = sum((preds - mean(obs))^2)
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SSerr = sum((obs - preds)^2)
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explainedVariance = SSreg / length(obs)
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explainedVariance
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> [1] 8.796875
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meanAbsoluteError = mean(abs(preds - obs))
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meanAbsoluteError
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> [1] 0.5
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meanSquaredError = mean((preds - obs)^2)
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meanSquaredError
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> [1] 0.3125
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rmse = sqrt(meanSquaredError)
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rmse
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> [1] 0.559017
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r2 = 1 - SSerr / SStot
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r2
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> [1] 0.9571734
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*/
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val predictionAndObservations = sc.parallelize(
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Seq((2.25, 3.0), (-0.25, -0.5), (1.75, 2.0), (7.75, 7.0)), 2)
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val metrics = new RegressionMetrics(predictionAndObservations)
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assert(metrics.explainedVariance ~== 8.79687 absTol 1E-5,
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"explained variance regression score mismatch")
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assert(metrics.meanAbsoluteError ~== 0.5 absTol 1E-5, "mean absolute error mismatch")
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assert(metrics.meanSquaredError ~== 0.3125 absTol 1E-5, "mean squared error mismatch")
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assert(metrics.rootMeanSquaredError ~== 0.55901 absTol 1E-5,
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"root mean squared error mismatch")
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assert(metrics.r2 ~== 0.95717 absTol 1E-5, "r2 score mismatch")
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}
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test("regression metrics for biased (no intercept term) predictor") {
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/* Verify results in R:
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preds = c(2.5, 0.0, 2.0, 8.0)
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obs = c(3.0, -0.5, 2.0, 7.0)
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SStot = sum((obs - mean(obs))^2)
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SSreg = sum((preds - mean(obs))^2)
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SSerr = sum((obs - preds)^2)
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explainedVariance = SSreg / length(obs)
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explainedVariance
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> [1] 8.859375
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meanAbsoluteError = mean(abs(preds - obs))
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meanAbsoluteError
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> [1] 0.5
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meanSquaredError = mean((preds - obs)^2)
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meanSquaredError
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> [1] 0.375
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rmse = sqrt(meanSquaredError)
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rmse
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> [1] 0.6123724
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r2 = 1 - SSerr / SStot
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r2
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> [1] 0.9486081
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*/
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val predictionAndObservations = sc.parallelize(
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Seq((2.5, 3.0), (0.0, -0.5), (2.0, 2.0), (8.0, 7.0)), 2)
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val metrics = new RegressionMetrics(predictionAndObservations)
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assert(metrics.explainedVariance ~== 0.95717 absTol 1E-5,
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assert(metrics.explainedVariance ~== 8.85937 absTol 1E-5,
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"explained variance regression score mismatch")
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assert(metrics.meanAbsoluteError ~== 0.5 absTol 1E-5, "mean absolute error mismatch")
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assert(metrics.meanSquaredError ~== 0.375 absTol 1E-5, "mean squared error mismatch")
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assert(metrics.rootMeanSquaredError ~== 0.61237 absTol 1E-5,
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"root mean squared error mismatch")
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assert(metrics.r2 ~== 0.94861 absTol 1E-5, "r2 score mismatch")
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assert(metrics.r2 ~== 0.94860 absTol 1E-5, "r2 score mismatch")
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}
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test("regression metrics with complete fitting") {
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val predictionAndObservations = sc.parallelize(
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Seq((3.0, 3.0), (0.0, 0.0), (2.0, 2.0), (8.0, 8.0)), 2)
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val metrics = new RegressionMetrics(predictionAndObservations)
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assert(metrics.explainedVariance ~== 1.0 absTol 1E-5,
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assert(metrics.explainedVariance ~== 8.6875 absTol 1E-5,
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"explained variance regression score mismatch")
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assert(metrics.meanAbsoluteError ~== 0.0 absTol 1E-5, "mean absolute error mismatch")
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assert(metrics.meanSquaredError ~== 0.0 absTol 1E-5, "mean squared error mismatch")
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@ -82,7 +82,7 @@ class RegressionMetrics(JavaModelWrapper):
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... (2.5, 3.0), (0.0, -0.5), (2.0, 2.0), (8.0, 7.0)])
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>>> metrics = RegressionMetrics(predictionAndObservations)
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>>> metrics.explainedVariance
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0.95...
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8.859...
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>>> metrics.meanAbsoluteError
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0.5...
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>>> metrics.meanSquaredError
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