Adding Linear Regression, and refactoring Ridge Regression.

4 files changed, 384 insertions, 158 deletions

diff --git a/mllib/src/main/scala/spark/mllib/regression/LinearRegression.scala b/mllib/src/main/scala/spark/mllib/regression/LinearRegression.scala
new file mode 100644
index 0000000000..0ea5348a1f
--- /dev/null
+++ b/mllib/src/main/scala/spark/mllib/regression/LinearRegression.scala
@@ -0,0 +1,168 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package spark.mllib.regression
+
+import spark.{Logging, RDD, SparkContext}
+import spark.mllib.optimization._
+import spark.mllib.util.MLUtils
+
+import org.jblas.DoubleMatrix
+
+/**
+ * Regression model trained using LinearRegression.
+ *
+ * @param weights Weights computed for every feature.
+ * @param intercept Intercept computed for this model.
+ */
+class LinearRegressionModel(
+                  override val weights: Array[Double],
+                  override val intercept: Double)
+  extends GeneralizedLinearModel(weights, intercept)
+  with RegressionModel with Serializable {
+
+  override def predictPoint(dataMatrix: DoubleMatrix, weightMatrix: DoubleMatrix,
+                            intercept: Double) = {
+    dataMatrix.dot(weightMatrix) + intercept
+  }
+}
+
+/**
+ * Train a regression model with no regularization using Stochastic Gradient Descent.
+ */
+class LinearRegressionWithSGD private (
+                             var stepSize: Double,
+                             var numIterations: Int,
+                             var miniBatchFraction: Double,
+                             var addIntercept: Boolean)
+  extends GeneralizedLinearAlgorithm[LinearRegressionModel]
+  with Serializable {
+
+  val gradient = new SquaredGradient()
+  val updater = new SimpleUpdater()
+  val optimizer = new GradientDescent(gradient, updater).setStepSize(stepSize)
+    .setNumIterations(numIterations)
+    .setMiniBatchFraction(miniBatchFraction)
+
+  /**
+   * Construct a LinearRegression object with default parameters
+   */
+  def this() = this(1.0, 100, 1.0, true)
+
+  def createModel(weights: Array[Double], intercept: Double) = {
+    new LinearRegressionModel(weights, intercept)
+  }
+}
+
+/**
+ * Top-level methods for calling LinearRegression.
+ */
+object LinearRegressionWithSGD {
+
+  /**
+   * Train a Linear Regression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. Each iteration uses
+   * `miniBatchFraction` fraction of the data to calculate the gradient. The weights used in
+   * gradient descent are initialized using the initial weights provided.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @param stepSize Step size to be used for each iteration of gradient descent.
+   * @param miniBatchFraction Fraction of data to be used per iteration.
+   * @param initialWeights Initial set of weights to be used. Array should be equal in size to 
+   *        the number of features in the data.
+   */
+  def train(
+             input: RDD[LabeledPoint],
+             numIterations: Int,
+             stepSize: Double,
+             miniBatchFraction: Double,
+             initialWeights: Array[Double])
+  : LinearRegressionModel =
+  {
+    new LinearRegressionWithSGD(stepSize, numIterations, miniBatchFraction, true).run(input,
+      initialWeights)
+  }
+
+  /**
+   * Train a LinearRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. Each iteration uses
+   * `miniBatchFraction` fraction of the data to calculate the gradient.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @param stepSize Step size to be used for each iteration of gradient descent.
+   * @param miniBatchFraction Fraction of data to be used per iteration.
+   */
+  def train(
+             input: RDD[LabeledPoint],
+             numIterations: Int,
+             stepSize: Double,
+             miniBatchFraction: Double)
+  : LinearRegressionModel =
+  {
+    new LinearRegressionWithSGD(stepSize, numIterations, miniBatchFraction, true).run(input)
+  }
+
+  /**
+   * Train a LinearRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. We use the entire data set to
+   * update the gradient in each iteration.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param stepSize Step size to be used for each iteration of Gradient Descent.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @return a LinearRegressionModel which has the weights and offset from training.
+   */
+  def train(
+             input: RDD[LabeledPoint],
+             numIterations: Int,
+             stepSize: Double)
+  : LinearRegressionModel =
+  {
+    train(input, numIterations, stepSize, 1.0)
+  }
+
+  /**
+   * Train a LinearRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using a step size of 1.0. We use the entire data set to
+   * update the gradient in each iteration.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @return a LinearRegressionModel which has the weights and offset from training.
+   */
+  def train(
+             input: RDD[LabeledPoint],
+             numIterations: Int)
+  : LinearRegressionModel =
+  {
+    train(input, numIterations, 1.0, 1.0)
+  }
+
+  def main(args: Array[String]) {
+    if (args.length != 5) {
+      println("Usage: LinearRegression <master> <input_dir> <step_size> <niters>")
+      System.exit(1)
+    }
+    val sc = new SparkContext(args(0), "LinearRegression")
+    val data = MLUtils.loadLabeledData(sc, args(1))
+    val model = LinearRegressionWithSGD.train(data, args(3).toInt, args(2).toDouble)
+
+    sc.stop()
+  }
+}
diff --git a/mllib/src/main/scala/spark/mllib/regression/RidgeRegression.scala b/mllib/src/main/scala/spark/mllib/regression/RidgeRegression.scala
index b42d94af41..addf8cd59e 100644
--- a/mllib/src/main/scala/spark/mllib/regression/RidgeRegression.scala
+++ b/mllib/src/main/scala/spark/mllib/regression/RidgeRegression.scala
@@ -18,200 +18,159 @@
 package spark.mllib.regression
 
 import spark.{Logging, RDD, SparkContext}
+import spark.mllib.optimization._
 import spark.mllib.util.MLUtils
 
 import org.jblas.DoubleMatrix
-import org.jblas.Solve
-
-import scala.annotation.tailrec
-import scala.collection.mutable
 
 /**
- * Ridge Regression from Joseph Gonzalez's implementation in MLBase
+ * Regression model trained using RidgeRegression.
+ *
+ * @param weights Weights computed for every feature.
+ * @param intercept Intercept computed for this model.
  */
 class RidgeRegressionModel(
-    val weights: DoubleMatrix,
-    val intercept: Double,
-    val lambdaOpt: Double,
-    val lambdas: Seq[(Double, Double, DoubleMatrix)])
-  extends RegressionModel {
-
-  override def predict(testData: RDD[Array[Double]]): RDD[Double] = {
-    // A small optimization to avoid serializing the entire model.
-    val localIntercept = this.intercept
-    val localWeights = this.weights
-    testData.map { x =>
-      (new DoubleMatrix(1, x.length, x:_*).mmul(localWeights)).get(0) + localIntercept
-    }
-  }
-
-  override def predict(testData: Array[Double]): Double = {
-    (new DoubleMatrix(1, testData.length, testData:_*).mmul(this.weights)).get(0) + this.intercept
+    override val weights: Array[Double],
+    override val intercept: Double)
+  extends GeneralizedLinearModel(weights, intercept)
+  with RegressionModel with Serializable {
+
+  override def predictPoint(dataMatrix: DoubleMatrix, weightMatrix: DoubleMatrix,
+                            intercept: Double) = {
+    dataMatrix.dot(weightMatrix) + intercept
   }
 }
 
-class RidgeRegression private (var lambdaLow: Double, var lambdaHigh: Double)
-  extends Logging {
-
-  def this() = this(0.0, 100.0)
+/**
+ * Train a regression model with L2-regularization using Stochastic Gradient Descent.
+ */
+class RidgeRegressionWithSGD private (
+    var stepSize: Double,
+    var numIterations: Int,
+    var regParam: Double,
+    var miniBatchFraction: Double,
+    var addIntercept: Boolean)
+    extends GeneralizedLinearAlgorithm[RidgeRegressionModel]
+  with Serializable {
+
+  val gradient = new SquaredGradient()
+  val updater = new SquaredL2Updater()
+  val optimizer = new GradientDescent(gradient, updater).setStepSize(stepSize)
+    .setNumIterations(numIterations)
+    .setRegParam(regParam)
+    .setMiniBatchFraction(miniBatchFraction)
 
   /**
-   * Set the lower bound on binary search for lambda's. Default is 0.
+   * Construct a RidgeRegression object with default parameters
    */
-  def setLowLambda(low: Double) = {
-    this.lambdaLow = low
-    this
+  def this() = this(1.0, 100, 1.0, 1.0, true)
+
+  def createModel(weights: Array[Double], intercept: Double) = {
+    new RidgeRegressionModel(weights, intercept)
   }
+}
+
+/**
+ * Top-level methods for calling RidgeRegression.
+ */
+object RidgeRegressionWithSGD {
 
   /**
-   * Set the upper bound on binary search for lambda's. Default is 100.0.
+   * Train a RidgeRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. Each iteration uses
+   * `miniBatchFraction` fraction of the data to calculate the gradient. The weights used in
+   * gradient descent are initialized using the initial weights provided.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @param stepSize Step size to be used for each iteration of gradient descent.
+   * @param regParam Regularization parameter.
+   * @param miniBatchFraction Fraction of data to be used per iteration.
+   * @param initialWeights Initial set of weights to be used. Array should be equal in size to 
+   *        the number of features in the data.
    */
-  def setHighLambda(hi: Double) = {
-    this.lambdaHigh = hi
-    this
+  def train(
+    input: RDD[LabeledPoint],
+    numIterations: Int,
+    stepSize: Double,
+    regParam: Double,
+    miniBatchFraction: Double,
+    initialWeights: Array[Double])
+  : RidgeRegressionModel =
+  {
+    new RidgeRegressionWithSGD(stepSize, numIterations, regParam, miniBatchFraction, true).run(input,
+      initialWeights)
   }
 
-  def train(inputLabeled: RDD[LabeledPoint]): RidgeRegressionModel = {
-    val input = inputLabeled.map(labeledPoint => (labeledPoint.label, labeledPoint.features))
-    val nfeatures: Int = input.take(1)(0)._2.length
-    val nexamples: Long = input.count()
-
-    val (yMean, xColMean, xColSd) = MLUtils.computeStats(input, nfeatures, nexamples)
-
-    val data = input.map { case(y, features) =>
-      val yNormalized = y - yMean
-      val featuresMat = new DoubleMatrix(nfeatures, 1, features:_*)
-      val featuresNormalized = featuresMat.sub(xColMean).divi(xColSd)
-      (yNormalized, featuresNormalized.toArray)
-    }
-
-    // Compute XtX - Size of XtX is nfeatures by nfeatures
-    val XtX: DoubleMatrix = data.map { case (y, features) =>
-      val x = new DoubleMatrix(1, features.length, features:_*)
-      x.transpose().mmul(x)
-    }.reduce(_.addi(_))
-
-    // Compute Xt*y - Size of Xty is nfeatures by 1
-    val Xty: DoubleMatrix = data.map { case (y, features) =>
-      new DoubleMatrix(features.length, 1, features:_*).mul(y)
-    }.reduce(_.addi(_))
-
-    // Define a function to compute the leave one out cross validation error
-    // for a single example
-    def crossValidate(lambda: Double): (Double, Double, DoubleMatrix) = {
-      // Compute the MLE ridge regression parameter value
-
-      // Ridge Regression parameter = inv(XtX + \lambda*I) * Xty
-      val XtXlambda = DoubleMatrix.eye(nfeatures).muli(lambda).addi(XtX)
-      val w = Solve.solveSymmetric(XtXlambda, Xty)
-
-      val invXtX = Solve.solveSymmetric(XtXlambda, DoubleMatrix.eye(nfeatures))
-
-      // compute the generalized cross validation score
-      val cverror = data.map {
-        case (y, features) =>
-          val x = new DoubleMatrix(features.length, 1, features:_*)
-          val yhat = w.transpose().mmul(x).get(0)
-          val H_ii = x.transpose().mmul(invXtX).mmul(x).get(0)
-          val residual = (y - yhat) / (1.0 - H_ii)
-          residual * residual
-      }.reduce(_ + _) / nexamples
-
-      (lambda, cverror, w)
-    }
-
-    // Binary search for the best assignment to lambda.
-    def binSearch(low: Double, high: Double): Seq[(Double, Double, DoubleMatrix)] = {
-      val buffer = mutable.ListBuffer.empty[(Double, Double, DoubleMatrix)]
-
-      @tailrec
-      def loop(low: Double, high: Double): Seq[(Double, Double, DoubleMatrix)] = {
-        val mid = (high - low) / 2 + low
-        val lowValue = crossValidate((mid - low) / 2 + low)
-        val highValue = crossValidate((high - mid) / 2 + mid)
-        val (newLow, newHigh) = if (lowValue._2 < highValue._2) {
-          (low, mid + (high-low)/4)
-        } else {
-          (mid - (high-low)/4, high)
-        }
-        if (newHigh - newLow > 1.0E-7) {
-          buffer += lowValue += highValue
-          loop(newLow, newHigh)
-        } else {
-          buffer += lowValue += highValue
-          buffer.result()
-        }
-      }
-
-      loop(low, high)
-    }
-
-    // Actually compute the best lambda
-    val lambdas = binSearch(lambdaLow, lambdaHigh).sortBy(_._1)
-
-    // Find the best parameter set by taking the lowest cverror.
-    val (lambdaOpt, cverror, weights) = lambdas.reduce((a, b) => if (a._2 < b._2) a else b)
-
-    // Return the model which contains the solution
-    val weightsScaled = weights.div(xColSd)
-    val intercept = yMean - (weights.transpose().mmul(xColMean.div(xColSd)).get(0))
-    val model = new RidgeRegressionModel(weightsScaled, intercept, lambdaOpt, lambdas)
-
-    logInfo("RidgeRegression: optimal lambda " + model.lambdaOpt)
-    logInfo("RidgeRegression: optimal weights " + model.weights)
-    logInfo("RidgeRegression: optimal intercept " + model.intercept)
-    logInfo("RidgeRegression: cross-validation error " + cverror)
-
-    model
+  /**
+   * Train a RidgeRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. Each iteration uses
+   * `miniBatchFraction` fraction of the data to calculate the gradient.
+   *
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @param stepSize Step size to be used for each iteration of gradient descent.
+   * @param regParam Regularization parameter.
+   * @param miniBatchFraction Fraction of data to be used per iteration.
+   */
+  def train(
+    input: RDD[LabeledPoint],
+    numIterations: Int,
+    stepSize: Double,
+    regParam: Double,
+    miniBatchFraction: Double)
+  : RidgeRegressionModel =
+  {
+    new RidgeRegressionWithSGD(stepSize, numIterations, regParam, miniBatchFraction, true).run(input)
   }
-}
-
-/**
- * Top-level methods for calling Ridge Regression.
- */
-object RidgeRegression {
-  // NOTE(shivaram): We use multiple train methods instead of default arguments to support
-  // Java programs.
 
   /**
-   * Train a ridge regression model given an RDD of (response, features) pairs.
-   * We use the closed form solution to compute the cross-validation score for
-   * a given lambda. The optimal lambda is computed by performing binary search
-   * between the provided bounds of lambda.
+   * Train a RidgeRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using the specified step size. We use the entire data set to
+   * update the gradient in each iteration.
    *
-   * @param input RDD of (response, array of features) pairs.
-   * @param lambdaLow lower bound used in binary search for lambda
-   * @param lambdaHigh upper bound used in binary search for lambda
+   * @param input RDD of (label, array of features) pairs.
+   * @param stepSize Step size to be used for each iteration of Gradient Descent.
+   * @param regParam Regularization parameter.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @return a RidgeRegressionModel which has the weights and offset from training.
    */
   def train(
-      input: RDD[LabeledPoint],
-      lambdaLow: Double,
-      lambdaHigh: Double)
-    : RidgeRegressionModel =
+    input: RDD[LabeledPoint],
+    numIterations: Int,
+    stepSize: Double,
+    regParam: Double)
+  : RidgeRegressionModel =
   {
-    new RidgeRegression(lambdaLow, lambdaHigh).train(input)
+    train(input, numIterations, stepSize, regParam, 1.0)
   }
 
   /**
-   * Train a ridge regression model given an RDD of (response, features) pairs.
-   * We use the closed form solution to compute the cross-validation score for
-   * a given lambda. The optimal lambda is computed by performing binary search
-   * between lambda values of 0 and 100.
+   * Train a RidgeRegression model given an RDD of (label, features) pairs. We run a fixed number
+   * of iterations of gradient descent using a step size of 1.0. We use the entire data set to
+   * update the gradient in each iteration.
    *
-   * @param input RDD of (response, array of features) pairs.
+   * @param input RDD of (label, array of features) pairs.
+   * @param numIterations Number of iterations of gradient descent to run.
+   * @return a RidgeRegressionModel which has the weights and offset from training.
    */
-  def train(input: RDD[LabeledPoint]) : RidgeRegressionModel = {
-    train(input, 0.0, 100.0)
+  def train(
+    input: RDD[LabeledPoint],
+    numIterations: Int)
+  : RidgeRegressionModel =
+  {
+    train(input, numIterations, 1.0, 1.0, 1.0)
   }
 
   def main(args: Array[String]) {
-    if (args.length != 2) {
-      println("Usage: RidgeRegression <master> <input_dir>")
+    if (args.length != 5) {
+      println("Usage: RidgeRegression <master> <input_dir> <step_size> <regularization_parameter> <niters>")
       System.exit(1)
     }
     val sc = new SparkContext(args(0), "RidgeRegression")
     val data = MLUtils.loadLabeledData(sc, args(1))
-    val model = RidgeRegression.train(data, 0, 1000)
+    val model = RidgeRegressionWithSGD.train(data, args(4).toInt, args(2).toDouble, args(3).toDouble)
+
     sc.stop()
   }
 }
diff --git a/mllib/src/main/scala/spark/mllib/util/LinearRegressionDataGenerator.scala b/mllib/src/main/scala/spark/mllib/util/LinearRegressionDataGenerator.scala
new file mode 100644
index 0000000000..39e2a30b55
--- /dev/null
+++ b/mllib/src/main/scala/spark/mllib/util/LinearRegressionDataGenerator.scala
@@ -0,0 +1,98 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package spark.mllib.util
+
+import scala.util.Random
+
+import org.jblas.DoubleMatrix
+
+import spark.{RDD, SparkContext}
+import spark.mllib.regression.LabeledPoint
+
+/**
+ * Generate sample data used for LinearRegression. This class generates
+ * uniformly random values for every feature and adds Gaussian noise with mean `eps` to the
+ * response variable `Y`.
+ *
+ */
+object LinearRegressionDataGenerator {
+
+  /**
+   * Generate an RDD containing sample data for LinearRegression.
+   *
+   * @param sc SparkContext to be used for generating the RDD.
+   * @param nexamples Number of examples that will be contained in the RDD.
+   * @param nfeatures Number of features to generate for each example.
+   * @param eps Epsilon factor by which examples are scaled.
+   * @param nparts Number of partitions in the RDD. Default value is 2.
+   *
+   * @return RDD of LabeledPoint containing sample data.
+   */
+  def generateLinearRDD(
+    sc: SparkContext,
+    nexamples: Int,
+    nfeatures: Int,
+    eps: Double,
+    nparts: Int = 2,
+    intercept: Double = 0.0) : RDD[LabeledPoint] = {
+    org.jblas.util.Random.seed(42)
+    // Random values distributed uniformly in [-0.5, 0.5]
+    val w = DoubleMatrix.rand(nfeatures, 1).subi(0.5)
+    w.put(0, 0, 10)
+    w.put(1, 0, 10)
+
+    val data: RDD[LabeledPoint] = sc.parallelize(0 until nparts, nparts).flatMap { p =>
+      org.jblas.util.Random.seed(42 + p)
+      val examplesInPartition = nexamples / nparts
+
+      val X = DoubleMatrix.rand(examplesInPartition, nfeatures)
+      val y = X.mmul(w).add(intercept)
+
+      val rnd = new Random(42 + p)
+
+      val normalValues = Array.fill[Double](examplesInPartition)(rnd.nextGaussian() * eps)
+      val yObs = new DoubleMatrix(normalValues).addi(y)
+
+      Iterator.tabulate(examplesInPartition) { i =>
+        LabeledPoint(yObs.get(i, 0), X.getRow(i).toArray)
+      }
+    }
+    data
+  }
+
+  def main(args: Array[String]) {
+    if (args.length < 2) {
+      println("Usage: LinearRegressionGenerator " +
+        "<master> <output_dir> [num_examples] [num_features] [num_partitions]")
+      System.exit(1)
+    }
+
+    val sparkMaster: String = args(0)
+    val outputPath: String = args(1)
+    val nexamples: Int = if (args.length > 2) args(2).toInt else 1000
+    val nfeatures: Int = if (args.length > 3) args(3).toInt else 100
+    val parts: Int = if (args.length > 4) args(4).toInt else 2
+    val eps = 10
+
+    val sc = new SparkContext(sparkMaster, "LinearRegressionDataGenerator")
+    val data = generateLinearRDD(sc, nexamples, nfeatures, eps, parts)
+
+    MLUtils.saveLabeledData(data, outputPath)
+    sc.stop()
+  }
+}
diff --git a/mllib/src/main/scala/spark/mllib/util/RidgeRegressionDataGenerator.scala b/mllib/src/main/scala/spark/mllib/util/RidgeRegressionDataGenerator.scala
index 4d329168be..08dce723b8 100644
--- a/mllib/src/main/scala/spark/mllib/util/RidgeRegressionDataGenerator.scala
+++ b/mllib/src/main/scala/spark/mllib/util/RidgeRegressionDataGenerator.scala
@@ -48,7 +48,8 @@ object RidgeRegressionDataGenerator {
     nexamples: Int,
     nfeatures: Int,
     eps: Double,
-    nparts: Int = 2) : RDD[LabeledPoint] = {
+    nparts: Int = 2,
+    intercept: Double = 0.0) : RDD[LabeledPoint] = {
     org.jblas.util.Random.seed(42)
     // Random values distributed uniformly in [-0.5, 0.5]
     val w = DoubleMatrix.rand(nfeatures, 1).subi(0.5)
@@ -60,7 +61,7 @@ object RidgeRegressionDataGenerator {
       val examplesInPartition = nexamples / nparts
 
       val X = DoubleMatrix.rand(examplesInPartition, nfeatures)
-      val y = X.mmul(w)
+      val y = X.mmul(w).add(intercept)
 
       val rnd = new Random(42 + p)