[SPARK-12732][ML] bug fix in linear regression train

Fixed the bug in linear regression train for the case when the target variable is constant. The two cases for `fitIntercept=true` or `fitIntercept=false` should be treated differently.

Author: Imran Younus <iyounus@us.ibm.com>

Closes #10702 from iyounus/SPARK-12732_bug_fix_in_linear_regression_train.

1 files changed, 105 insertions, 0 deletions

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 273c882c2a..81fc6603cc 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
@@ -37,6 +37,8 @@ class LinearRegressionSuite
   @transient var datasetWithDenseFeatureWithoutIntercept: DataFrame = _
   @transient var datasetWithSparseFeature: DataFrame = _
   @transient var datasetWithWeight: DataFrame = _
+  @transient var datasetWithWeightConstantLabel: DataFrame = _
+  @transient var datasetWithWeightZeroLabel: DataFrame = _
 
   /*
      In `LinearRegressionSuite`, we will make sure that the model trained by SparkML
@@ -92,6 +94,29 @@ class LinearRegressionSuite
         Instance(23.0, 3.0, Vectors.dense(2.0, 11.0)),
         Instance(29.0, 4.0, Vectors.dense(3.0, 13.0))
       ), 2))
+
+    /*
+       R code:
+
+       A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
+       b.const <- c(17, 17, 17, 17)
+       w <- c(1, 2, 3, 4)
+       df.const.label <- as.data.frame(cbind(A, b.const))
+     */
+    datasetWithWeightConstantLabel = sqlContext.createDataFrame(
+      sc.parallelize(Seq(
+        Instance(17.0, 1.0, Vectors.dense(0.0, 5.0).toSparse),
+        Instance(17.0, 2.0, Vectors.dense(1.0, 7.0)),
+        Instance(17.0, 3.0, Vectors.dense(2.0, 11.0)),
+        Instance(17.0, 4.0, Vectors.dense(3.0, 13.0))
+      ), 2))
+    datasetWithWeightZeroLabel = sqlContext.createDataFrame(
+      sc.parallelize(Seq(
+        Instance(0.0, 1.0, Vectors.dense(0.0, 5.0).toSparse),
+        Instance(0.0, 2.0, Vectors.dense(1.0, 7.0)),
+        Instance(0.0, 3.0, Vectors.dense(2.0, 11.0)),
+        Instance(0.0, 4.0, Vectors.dense(3.0, 13.0))
+      ), 2))
   }
 
   test("params") {
@@ -558,6 +583,86 @@ class LinearRegressionSuite
     }
   }
 
+  test("linear regression model with constant label") {
+    /*
+       R code:
+       for (formula in c(b.const ~ . -1, b.const ~ .)) {
+         model <- lm(formula, data=df.const.label, weights=w)
+         print(as.vector(coef(model)))
+       }
+      [1] -9.221298  3.394343
+      [1] 17  0  0
+    */
+    val expected = Seq(
+      Vectors.dense(0.0, -9.221298, 3.394343),
+      Vectors.dense(17.0, 0.0, 0.0))
+
+    Seq("auto", "l-bfgs", "normal").foreach { solver =>
+      var idx = 0
+      for (fitIntercept <- Seq(false, true)) {
+        val model1 = new LinearRegression()
+          .setFitIntercept(fitIntercept)
+          .setWeightCol("weight")
+          .setSolver(solver)
+          .fit(datasetWithWeightConstantLabel)
+        val actual1 = Vectors.dense(model1.intercept, model1.coefficients(0),
+            model1.coefficients(1))
+        assert(actual1 ~== expected(idx) absTol 1e-4)
+
+        val model2 = new LinearRegression()
+          .setFitIntercept(fitIntercept)
+          .setWeightCol("weight")
+          .setSolver(solver)
+          .fit(datasetWithWeightZeroLabel)
+        val actual2 = Vectors.dense(model2.intercept, model2.coefficients(0),
+            model2.coefficients(1))
+        assert(actual2 ~==  Vectors.dense(0.0, 0.0, 0.0) absTol 1e-4)
+        idx += 1
+      }
+    }
+  }
+
+  test("regularized linear regression through origin with constant label") {
+    // The problem is ill-defined if fitIntercept=false, regParam is non-zero.
+    // An exception is thrown in this case.
+    Seq("auto", "l-bfgs", "normal").foreach { solver =>
+      for (standardization <- Seq(false, true)) {
+        val model = new LinearRegression().setFitIntercept(false)
+          .setRegParam(0.1).setStandardization(standardization).setSolver(solver)
+        intercept[IllegalArgumentException] {
+          model.fit(datasetWithWeightConstantLabel)
+        }
+      }
+    }
+  }
+
+  test("linear regression with l-bfgs when training is not needed") {
+    // When label is constant, l-bfgs solver returns results without training.
+    // There are two possibilities: If the label is non-zero but constant,
+    // and fitIntercept is true, then the model return yMean as intercept without training.
+    // If label is all zeros, then all coefficients are zero regardless of fitIntercept, so
+    // no training is needed.
+    for (fitIntercept <- Seq(false, true)) {
+      for (standardization <- Seq(false, true)) {
+        val model1 = new LinearRegression()
+          .setFitIntercept(fitIntercept)
+          .setStandardization(standardization)
+          .setWeightCol("weight")
+          .setSolver("l-bfgs")
+          .fit(datasetWithWeightConstantLabel)
+        if (fitIntercept) {
+          assert(model1.summary.objectiveHistory(0) ~== 0.0 absTol 1e-4)
+        }
+        val model2 = new LinearRegression()
+          .setFitIntercept(fitIntercept)
+          .setWeightCol("weight")
+          .setSolver("l-bfgs")
+          .fit(datasetWithWeightZeroLabel)
+        assert(model2.summary.objectiveHistory(0) ~== 0.0 absTol 1e-4)
+      }
+    }
+  }
+
   test("linear regression model training summary") {
     Seq("auto", "l-bfgs", "normal").foreach { solver =>
       val trainer = new LinearRegression().setSolver(solver)