[SPARK-9090] [ML] Fix definition of residual in LinearRegressionSummary, EnsembleTestHelper, and SquaredError

Make the definition of residuals in Spark consistent with literature. We have been using `prediction - label` for residuals, but literature usually defines `residual = label - prediction`.

Author: Feynman Liang <fliang@databricks.com>

Closes #7435 from feynmanliang/SPARK-9090-Fix-LinearRegressionSummary-Residuals and squashes the following commits:

f4b39d8 [Feynman Liang] Fix doc
bc12a92 [Feynman Liang] Tweak EnsembleTestHelper and SquaredError residuals
63f0d60 [Feynman Liang] Fix definition of residual

4 files changed, 7 insertions, 7 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/ml/regression/LinearRegression.scala b/mllib/src/main/scala/org/apache/spark/ml/regression/LinearRegression.scala
index 8fc9860566..89718e0f3e 100644
--- a/mllib/src/main/scala/org/apache/spark/ml/regression/LinearRegression.scala
+++ b/mllib/src/main/scala/org/apache/spark/ml/regression/LinearRegression.scala
@@ -355,9 +355,9 @@ class LinearRegressionSummary private[regression] (
    */
   val r2: Double = metrics.r2
 
-  /** Residuals (predicted value - label value) */
+  /** Residuals (label - predicted value) */
   @transient lazy val residuals: DataFrame = {
-    val t = udf { (pred: Double, label: Double) => pred - label}
+    val t = udf { (pred: Double, label: Double) => label - pred }
     predictions.select(t(col(predictionCol), col(labelCol)).as("residuals"))
   }
 
diff --git a/mllib/src/main/scala/org/apache/spark/mllib/tree/loss/SquaredError.scala b/mllib/src/main/scala/org/apache/spark/mllib/tree/loss/SquaredError.scala
index a5582d3ef3..011a5d5742 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/tree/loss/SquaredError.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/tree/loss/SquaredError.scala
@@ -42,11 +42,11 @@ object SquaredError extends Loss {
    * @return Loss gradient
    */
   override def gradient(prediction: Double, label: Double): Double = {
-    2.0 * (prediction - label)
+    - 2.0 * (label - prediction)
   }
 
   override private[mllib] def computeError(prediction: Double, label: Double): Double = {
-    val err = prediction - label
+    val err = label - prediction
     err * err
   }
 }
diff --git a/mllib/src/test/scala/org/apache/spark/ml/regression/LinearRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/ml/regression/LinearRegressionSuite.scala
index cf120cf2a4..374002c5b4 100644
--- a/mllib/src/test/scala/org/apache/spark/ml/regression/LinearRegressionSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/ml/regression/LinearRegressionSuite.scala
@@ -302,7 +302,7 @@ class LinearRegressionSuite extends SparkFunSuite with MLlibTestSparkContext {
       .map { case Row(features: DenseVector, label: Double) =>
       val prediction =
         features(0) * model.weights(0) + features(1) * model.weights(1) + model.intercept
-      prediction - label
+      label - prediction
     }
       .zip(model.summary.residuals.map(_.getDouble(0)))
       .collect()
@@ -314,7 +314,7 @@ class LinearRegressionSuite extends SparkFunSuite with MLlibTestSparkContext {
        Use the following R code to generate model training results.
 
        predictions <- predict(fit, newx=features)
-       residuals <- predictions - label
+       residuals <- label - predictions
        > mean(residuals^2) # MSE
        [1] 0.009720325
        > mean(abs(residuals)) # MAD
diff --git a/mllib/src/test/scala/org/apache/spark/mllib/tree/EnsembleTestHelper.scala b/mllib/src/test/scala/org/apache/spark/mllib/tree/EnsembleTestHelper.scala
index 8972c229b7..334bf3790f 100644
--- a/mllib/src/test/scala/org/apache/spark/mllib/tree/EnsembleTestHelper.scala
+++ b/mllib/src/test/scala/org/apache/spark/mllib/tree/EnsembleTestHelper.scala
@@ -70,7 +70,7 @@ object EnsembleTestHelper {
       metricName: String = "mse") {
     val predictions = input.map(x => model.predict(x.features))
     val errors = predictions.zip(input.map(_.label)).map { case (prediction, label) =>
-      prediction - label
+      label - prediction
     }
     val metric = metricName match {
       case "mse" =>