[SPARK-1969][MLlib] Online summarizer APIs for mean, variance, min, and max

It basically moved the private ColumnStatisticsAggregator class from RowMatrix to public available DeveloperApi with documentation and unitests.

Changes:
1) Moved the private implementation from org.apache.spark.mllib.linalg.ColumnStatisticsAggregator to org.apache.spark.mllib.stat.MultivariateOnlineSummarizer
2) When creating OnlineSummarizer object, the number of columns is not needed in the constructor. It's determined when users add the first sample.
3) Added the APIs documentation for MultivariateOnlineSummarizer.
4) Added the unittests for MultivariateOnlineSummarizer.

Author: DB Tsai <dbtsai@dbtsai.com>

Closes #955 from dbtsai/dbtsai-summarizer and squashes the following commits:

b13ac90 [DB Tsai] dbtsai-summarizer

mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/RowMatrix.scala

@@ -28,138 +28,7 @@ import org.apache.spark.annotation.Experimental
 import org.apache.spark.mllib.linalg._
 import org.apache.spark.rdd.RDD
 import org.apache.spark.Logging
-import org.apache.spark.mllib.stat.MultivariateStatisticalSummary
-
-/**
- * Column statistics aggregator implementing
- * [[org.apache.spark.mllib.stat.MultivariateStatisticalSummary]]
- * together with add() and merge() function.
- * A numerically stable algorithm is implemented to compute sample mean and variance:
- * [[http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance variance-wiki]].
- * Zero elements (including explicit zero values) are skipped when calling add() and merge(),
- * to have time complexity O(nnz) instead of O(n) for each column.
- */
-private class ColumnStatisticsAggregator(private val n: Int)
-    extends MultivariateStatisticalSummary with Serializable {
-
-  private val currMean: BDV[Double] = BDV.zeros[Double](n)
-  private val currM2n: BDV[Double] = BDV.zeros[Double](n)
-  private var totalCnt = 0.0
-  private val nnz: BDV[Double] = BDV.zeros[Double](n)
-  private val currMax: BDV[Double] = BDV.fill(n)(Double.MinValue)
-  private val currMin: BDV[Double] = BDV.fill(n)(Double.MaxValue)
-
-  override def mean: Vector = {
-    val realMean = BDV.zeros[Double](n)
-    var i = 0
-    while (i < n) {
-      realMean(i) = currMean(i) * nnz(i) / totalCnt
-      i += 1
-    }
-    Vectors.fromBreeze(realMean)
-  }
-
-  override def variance: Vector = {
-    val realVariance = BDV.zeros[Double](n)
-
-    val denominator = totalCnt - 1.0
-
-    // Sample variance is computed, if the denominator is less than 0, the variance is just 0.
-    if (denominator > 0.0) {
-      val deltaMean = currMean
-      var i = 0
-      while (i < currM2n.size) {
-        realVariance(i) =
-          currM2n(i) + deltaMean(i) * deltaMean(i) * nnz(i) * (totalCnt - nnz(i)) / totalCnt
-        realVariance(i) /= denominator
-        i += 1
-      }
-    }
-
-    Vectors.fromBreeze(realVariance)
-  }
-
-  override def count: Long = totalCnt.toLong
-
-  override def numNonzeros: Vector = Vectors.fromBreeze(nnz)
-
-  override def max: Vector = {
-    var i = 0
-    while (i < n) {
-      if ((nnz(i) < totalCnt) && (currMax(i) < 0.0)) currMax(i) = 0.0
-      i += 1
-    }
-    Vectors.fromBreeze(currMax)
-  }
-
-  override def min: Vector = {
-    var i = 0
-    while (i < n) {
-      if ((nnz(i) < totalCnt) && (currMin(i) > 0.0)) currMin(i) = 0.0
-      i += 1
-    }
-    Vectors.fromBreeze(currMin)
-  }
-
-  /**
-   * Aggregates a row.
-   */
-  def add(currData: BV[Double]): this.type = {
-    currData.activeIterator.foreach {
-      case (_, 0.0) => // Skip explicit zero elements.
-      case (i, value) =>
-        if (currMax(i) < value) {
-          currMax(i) = value
-        }
-        if (currMin(i) > value) {
-          currMin(i) = value
-        }
-
-        val tmpPrevMean = currMean(i)
-        currMean(i) = (currMean(i) * nnz(i) + value) / (nnz(i) + 1.0)
-        currM2n(i) += (value - currMean(i)) * (value - tmpPrevMean)
-
-        nnz(i) += 1.0
-    }
-
-    totalCnt += 1.0
-    this
-  }
-
-  /**
-   * Merges another aggregator.
-   */
-  def merge(other: ColumnStatisticsAggregator): this.type = {
-    require(n == other.n, s"Dimensions mismatch. Expecting $n but got ${other.n}.")
-
-    totalCnt += other.totalCnt
-    val deltaMean = currMean - other.currMean
-
-    var i = 0
-    while (i < n) {
-      // merge mean together
-      if (other.currMean(i) != 0.0) {
-        currMean(i) = (currMean(i) * nnz(i) + other.currMean(i) * other.nnz(i)) /
-          (nnz(i) + other.nnz(i))
-      }
-      // merge m2n together
-      if (nnz(i) + other.nnz(i) != 0.0) {
-        currM2n(i) += other.currM2n(i) + deltaMean(i) * deltaMean(i) * nnz(i) * other.nnz(i) /
-          (nnz(i) + other.nnz(i))
-      }
-      if (currMax(i) < other.currMax(i)) {
-        currMax(i) = other.currMax(i)
-      }
-      if (currMin(i) > other.currMin(i)) {
-        currMin(i) = other.currMin(i)
-      }
-      i += 1
-    }
-
-    nnz += other.nnz
-    this
-  }
-}
+import org.apache.spark.mllib.stat.{MultivariateOnlineSummarizer, MultivariateStatisticalSummary}
 
 /**
  * :: Experimental ::
@@ -478,8 +347,7 @@ class RowMatrix(
    * Computes column-wise summary statistics.
    */
   def computeColumnSummaryStatistics(): MultivariateStatisticalSummary = {
-    val zeroValue = new ColumnStatisticsAggregator(numCols().toInt)
-    val summary = rows.map(_.toBreeze).aggregate[ColumnStatisticsAggregator](zeroValue)(
+    val summary = rows.aggregate[MultivariateOnlineSummarizer](new MultivariateOnlineSummarizer)(
       (aggregator, data) => aggregator.add(data),
       (aggregator1, aggregator2) => aggregator1.merge(aggregator2)
     )

mllib/src/main/scala/org/apache/spark/mllib/stat/MultivariateOnlineSummarizer.scala

+/*
+ * 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 org.apache.spark.mllib.stat
+
+import breeze.linalg.{DenseVector => BDV}
+
+import org.apache.spark.annotation.DeveloperApi
+import org.apache.spark.mllib.linalg.{Vectors, Vector}
+
+/**
+ * :: DeveloperApi ::
+ * MultivariateOnlineSummarizer implements [[MultivariateStatisticalSummary]] to compute the mean,
+ * variance, minimum, maximum, counts, and nonzero counts for samples in sparse or dense vector
+ * format in a online fashion.
+ *
+ * Two MultivariateOnlineSummarizer can be merged together to have a statistical summary of
+ * the corresponding joint dataset.
+ *
+ * A numerically stable algorithm is implemented to compute sample mean and variance:
+ * Reference: [[http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance variance-wiki]]
+ * Zero elements (including explicit zero values) are skipped when calling add(),
+ * to have time complexity O(nnz) instead of O(n) for each column.
+ */
+@DeveloperApi
+class MultivariateOnlineSummarizer extends MultivariateStatisticalSummary with Serializable {
+
+  private var n = 0
+  private var currMean: BDV[Double] = _
+  private var currM2n: BDV[Double] = _
+  private var totalCnt: Long = 0
+  private var nnz: BDV[Double] = _
+  private var currMax: BDV[Double] = _
+  private var currMin: BDV[Double] = _
+
+  /**
+   * Add a new sample to this summarizer, and update the statistical summary.
+   *
+   * @param sample The sample in dense/sparse vector format to be added into this summarizer.
+   * @return This MultivariateOnlineSummarizer object.
+   */
+  def add(sample: Vector): this.type = {
+    if (n == 0) {
+      require(sample.toBreeze.length > 0, s"Vector should have dimension larger than zero.")
+      n = sample.toBreeze.length
+
+      currMean = BDV.zeros[Double](n)
+      currM2n = BDV.zeros[Double](n)
+      nnz = BDV.zeros[Double](n)
+      currMax = BDV.fill(n)(Double.MinValue)
+      currMin = BDV.fill(n)(Double.MaxValue)
+    }
+
+    require(n == sample.toBreeze.length, s"Dimensions mismatch when adding new sample." +
+      s" Expecting $n but got ${sample.toBreeze.length}.")
+
+    sample.toBreeze.activeIterator.foreach {
+      case (_, 0.0) => // Skip explicit zero elements.
+      case (i, value) =>
+        if (currMax(i) < value) {
+          currMax(i) = value
+        }
+        if (currMin(i) > value) {
+          currMin(i) = value
+        }
+
+        val tmpPrevMean = currMean(i)
+        currMean(i) = (currMean(i) * nnz(i) + value) / (nnz(i) + 1.0)
+        currM2n(i) += (value - currMean(i)) * (value - tmpPrevMean)
+
+        nnz(i) += 1.0
+    }
+
+    totalCnt += 1
+    this
+  }
+
+  /**
+   * Merge another MultivariateOnlineSummarizer, and update the statistical summary.
+   * (Note that it's in place merging; as a result, `this` object will be modified.)
+   *
+   * @param other The other MultivariateOnlineSummarizer to be merged.
+   * @return This MultivariateOnlineSummarizer object.
+   */
+  def merge(other: MultivariateOnlineSummarizer): this.type = {
+   if (this.totalCnt != 0 && other.totalCnt != 0) {
+      require(n == other.n, s"Dimensions mismatch when merging with another summarizer. " +
+        s"Expecting $n but got ${other.n}.")
+      totalCnt += other.totalCnt
+      val deltaMean: BDV[Double] = currMean - other.currMean
+      var i = 0
+      while (i < n) {
+        // merge mean together
+        if (other.currMean(i) != 0.0) {
+          currMean(i) = (currMean(i) * nnz(i) + other.currMean(i) * other.nnz(i)) /
+            (nnz(i) + other.nnz(i))
+        }
+        // merge m2n together
+        if (nnz(i) + other.nnz(i) != 0.0) {
+          currM2n(i) += other.currM2n(i) + deltaMean(i) * deltaMean(i) * nnz(i) * other.nnz(i) /
+            (nnz(i) + other.nnz(i))
+        }
+        if (currMax(i) < other.currMax(i)) {
+          currMax(i) = other.currMax(i)
+        }
+        if (currMin(i) > other.currMin(i)) {
+          currMin(i) = other.currMin(i)
+        }
+        i += 1
+      }
+      nnz += other.nnz
+    } else if (totalCnt == 0 && other.totalCnt != 0) {
+      this.n = other.n
+      this.currMean = other.currMean.copy
+      this.currM2n = other.currM2n.copy
+      this.totalCnt = other.totalCnt
+      this.nnz = other.nnz.copy
+      this.currMax = other.currMax.copy
+      this.currMin = other.currMin.copy
+    }
+    this
+  }
+
+  override def mean: Vector = {
+    require(totalCnt > 0, s"Nothing has been added to this summarizer.")
+
+    val realMean = BDV.zeros[Double](n)
+    var i = 0
+    while (i < n) {
+      realMean(i) = currMean(i) * (nnz(i) / totalCnt)
+      i += 1
+    }
+    Vectors.fromBreeze(realMean)
+  }
+
+  override def variance: Vector = {
+    require(totalCnt > 0, s"Nothing has been added to this summarizer.")
+
+    val realVariance = BDV.zeros[Double](n)
+
+    val denominator = totalCnt - 1.0
+
+    // Sample variance is computed, if the denominator is less than 0, the variance is just 0.
+    if (denominator > 0.0) {
+      val deltaMean = currMean
+      var i = 0
+      while (i < currM2n.size) {
+        realVariance(i) =
+          currM2n(i) + deltaMean(i) * deltaMean(i) * nnz(i) * (totalCnt - nnz(i)) / totalCnt
+        realVariance(i) /= denominator
+        i += 1
+      }
+    }
+
+    Vectors.fromBreeze(realVariance)
+  }
+
+  override def count: Long = totalCnt
+
+  override def numNonzeros: Vector = {
+    require(totalCnt > 0, s"Nothing has been added to this summarizer.")
+
+    Vectors.fromBreeze(nnz)
+  }
+
+  override def max: Vector = {
+    require(totalCnt > 0, s"Nothing has been added to this summarizer.")
+
+    var i = 0
+    while (i < n) {
+      if ((nnz(i) < totalCnt) && (currMax(i) < 0.0)) currMax(i) = 0.0
+      i += 1
+    }
+    Vectors.fromBreeze(currMax)
+  }
+
+  override def min: Vector = {
+    require(totalCnt > 0, s"Nothing has been added to this summarizer.")
+
+    var i = 0
+    while (i < n) {
+      if ((nnz(i) < totalCnt) && (currMin(i) > 0.0)) currMin(i) = 0.0
+      i += 1
+    }
+    Vectors.fromBreeze(currMin)
+  }
+}

mllib/src/test/scala/org/apache/spark/mllib/stat/MultivariateOnlineSummarizerSuite.scala

+/*
+ * 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 org.apache.spark.mllib.stat
+
+import org.scalatest.FunSuite
+
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.TestingUtils._
+
+class MultivariateOnlineSummarizerSuite extends FunSuite {
+
+  test("basic error handing") {
+    val summarizer = new MultivariateOnlineSummarizer
+
+    assert(summarizer.count === 0, "should be zero since nothing is added.")
+
+    withClue("Getting numNonzeros from empty summarizer should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.numNonzeros
+      }
+    }
+
+    withClue("Getting variance from empty summarizer should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.variance
+      }
+    }
+
+    withClue("Getting mean from empty summarizer should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.mean
+      }
+    }
+
+    withClue("Getting max from empty summarizer should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.max
+      }
+    }
+
+    withClue("Getting min from empty summarizer should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.min
+      }
+    }
+
+    summarizer.add(Vectors.dense(-1.0, 2.0, 6.0)).add(Vectors.sparse(3, Seq((0, -2.0), (1, 6.0))))
+
+    withClue("Adding a new dense sample with different array size should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.add(Vectors.dense(3.0, 1.0))
+      }
+    }
+
+    withClue("Adding a new sparse sample with different array size should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.add(Vectors.sparse(5, Seq((0, -2.0), (1, 6.0))))
+      }
+    }
+
+    val summarizer2 = (new MultivariateOnlineSummarizer).add(Vectors.dense(1.0, -2.0, 0.0, 4.0))
+    withClue("Merging a new summarizer with different dimensions should throw exception.") {
+      intercept[IllegalArgumentException] {
+        summarizer.merge(summarizer2)
+      }
+    }
+  }
+
+  test("dense vector input") {
+    // For column 2, the maximum will be 0.0, and it's not explicitly added since we ignore all
+    // the zeros; it's a case we need to test. For column 3, the minimum will be 0.0 which we
+    // need to test as well.
+    val summarizer = (new MultivariateOnlineSummarizer)
+      .add(Vectors.dense(-1.0, 0.0, 6.0))
+      .add(Vectors.dense(3.0, -3.0, 0.0))
+
+    assert(summarizer.mean.almostEquals(Vectors.dense(1.0, -1.5, 3.0)), "mean mismatch")
+
+    assert(summarizer.min.almostEquals(Vectors.dense(-1.0, -3, 0.0)), "min mismatch")
+
+    assert(summarizer.max.almostEquals(Vectors.dense(3.0, 0.0, 6.0)), "max mismatch")
+
+    assert(summarizer.numNonzeros.almostEquals(Vectors.dense(2, 1, 1)), "numNonzeros mismatch")
+
+    assert(summarizer.variance.almostEquals(Vectors.dense(8.0, 4.5, 18.0)), "variance mismatch")
+
+    assert(summarizer.count === 2)
+  }
+
+  test("sparse vector input") {
+    val summarizer = (new MultivariateOnlineSummarizer)
+      .add(Vectors.sparse(3, Seq((0, -1.0), (2, 6.0))))
+      .add(Vectors.sparse(3, Seq((0, 3.0), (1, -3.0))))
+
+    assert(summarizer.mean.almostEquals(Vectors.dense(1.0, -1.5, 3.0)), "mean mismatch")
+
+    assert(summarizer.min.almostEquals(Vectors.dense(-1.0, -3, 0.0)), "min mismatch")
+
+    assert(summarizer.max.almostEquals(Vectors.dense(3.0, 0.0, 6.0)), "max mismatch")
+
+    assert(summarizer.numNonzeros.almostEquals(Vectors.dense(2, 1, 1)), "numNonzeros mismatch")
+
+    assert(summarizer.variance.almostEquals(Vectors.dense(8.0, 4.5, 18.0)), "variance mismatch")
+
+    assert(summarizer.count === 2)
+  }
+
+  test("mixing dense and sparse vector input") {
+    val summarizer = (new MultivariateOnlineSummarizer)
+      .add(Vectors.sparse(3, Seq((0, -2.0), (1, 2.3))))
+      .add(Vectors.dense(0.0, -1.0, -3.0))
+      .add(Vectors.sparse(3, Seq((1, -5.1))))
+      .add(Vectors.dense(3.8, 0.0, 1.9))
+      .add(Vectors.dense(1.7, -0.6, 0.0))
+      .add(Vectors.sparse(3, Seq((1, 1.9), (2, 0.0))))
+
+    assert(summarizer.mean.almostEquals(
+      Vectors.dense(0.583333333333, -0.416666666666, -0.183333333333)), "mean mismatch")
+
+    assert(summarizer.min.almostEquals(Vectors.dense(-2.0, -5.1, -3)), "min mismatch")
+
+    assert(summarizer.max.almostEquals(Vectors.dense(3.8, 2.3, 1.9)), "max mismatch")
+
+    assert(summarizer.numNonzeros.almostEquals(Vectors.dense(3, 5, 2)), "numNonzeros mismatch")
+
+    assert(summarizer.variance.almostEquals(
+      Vectors.dense(3.857666666666, 7.0456666666666, 2.48166666666666)), "variance mismatch")
+
+    assert(summarizer.count === 6)
+  }
+
+  test("merging two summarizers") {
+    val summarizer1 = (new MultivariateOnlineSummarizer)
+      .add(Vectors.sparse(3, Seq((0, -2.0), (1, 2.3))))
+      .add(Vectors.dense(0.0, -1.0, -3.0))
+
+    val summarizer2 = (new MultivariateOnlineSummarizer)
+      .add(Vectors.sparse(3, Seq((1, -5.1))))
+      .add(Vectors.dense(3.8, 0.0, 1.9))
+      .add(Vectors.dense(1.7, -0.6, 0.0))
+      .add(Vectors.sparse(3, Seq((1, 1.9), (2, 0.0))))
+
+    val summarizer = summarizer1.merge(summarizer2)
+
+    assert(summarizer.mean.almostEquals(
+      Vectors.dense(0.583333333333, -0.416666666666, -0.183333333333)), "mean mismatch")
+
+    assert(summarizer.min.almostEquals(Vectors.dense(-2.0, -5.1, -3)), "min mismatch")
+
+    assert(summarizer.max.almostEquals(Vectors.dense(3.8, 2.3, 1.9)), "max mismatch")
+
+    assert(summarizer.numNonzeros.almostEquals(Vectors.dense(3, 5, 2)), "numNonzeros mismatch")
+
+    assert(summarizer.variance.almostEquals(
+      Vectors.dense(3.857666666666, 7.0456666666666, 2.48166666666666)), "variance mismatch")
+
+    assert(summarizer.count === 6)
+  }
+
+  test("merging summarizer with empty summarizer") {
+    // If one of two is non-empty, this should return the non-empty summarizer.
+    // If both of them are empty, then just return the empty summarizer.
+    val summarizer1 = (new MultivariateOnlineSummarizer)
+      .add(Vectors.dense(0.0, -1.0, -3.0)).merge(new MultivariateOnlineSummarizer)
+    assert(summarizer1.count === 1)
+
+    val summarizer2 = (new MultivariateOnlineSummarizer)
+      .merge((new MultivariateOnlineSummarizer).add(Vectors.dense(0.0, -1.0, -3.0)))
+    assert(summarizer2.count === 1)
+
+    val summarizer3 = (new MultivariateOnlineSummarizer).merge(new MultivariateOnlineSummarizer)
+    assert(summarizer3.count === 0)
+
+    assert(summarizer1.mean.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "mean mismatch")
+
+    assert(summarizer2.mean.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "mean mismatch")
+
+    assert(summarizer1.min.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "min mismatch")
+
+    assert(summarizer2.min.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "min mismatch")
+
+    assert(summarizer1.max.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "max mismatch")
+
+    assert(summarizer2.max.almostEquals(Vectors.dense(0.0, -1.0, -3.0)), "max mismatch")
+
+    assert(summarizer1.numNonzeros.almostEquals(Vectors.dense(0, 1, 1)), "numNonzeros mismatch")
+
+    assert(summarizer2.numNonzeros.almostEquals(Vectors.dense(0, 1, 1)), "numNonzeros mismatch")
+
+    assert(summarizer1.variance.almostEquals(Vectors.dense(0, 0, 0)), "variance mismatch")
+
+    assert(summarizer2.variance.almostEquals(Vectors.dense(0, 0, 0)), "variance mismatch")
+  }
+}

mllib/src/test/scala/org/apache/spark/mllib/util/TestingUtils.scala

+/*
+ * 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 org.apache.spark.mllib.util
+
+import org.apache.spark.mllib.linalg.Vector
+
+object TestingUtils {
+
+  implicit class DoubleWithAlmostEquals(val x: Double) {
+    // An improved version of AlmostEquals would always divide by the larger number.
+    // This will avoid the problem of diving by zero.
+    def almostEquals(y: Double, epsilon: Double = 1E-10): Boolean = {
+      if(x == y) {
+        true
+      } else if(math.abs(x) > math.abs(y)) {
+        math.abs(x - y) / math.abs(x) < epsilon
+      } else {
+        math.abs(x - y) / math.abs(y) < epsilon
+      }
+    }
+  }
+
+  implicit class VectorWithAlmostEquals(val x: Vector) {
+    def almostEquals(y: Vector, epsilon: Double = 1E-10): Boolean = {
+      x.toArray.corresponds(y.toArray) {
+        _.almostEquals(_, epsilon)
+      }
+    }
+  }
+}

project/MimaExcludes.scala

@@ -75,6 +75,7 @@ object MimaExcludes {
             ProblemFilters.exclude[MissingMethodProblem](
               "org.apache.spark.mllib.recommendation.ALS.org$apache$spark$mllib$recommendation$ALS$$<init>$default$7")
           ) ++
+          MimaBuild.excludeSparkClass("mllib.linalg.distributed.ColumnStatisticsAggregator") ++
           MimaBuild.excludeSparkClass("rdd.ZippedRDD") ++
           MimaBuild.excludeSparkClass("rdd.ZippedPartition") ++
           MimaBuild.excludeSparkClass("util.SerializableHyperLogLog") ++