[SPARK-13019][DOCS] Replace example code in mllib-statistics.md using include_example

https://issues.apache.org/jira/browse/SPARK-13019

The example code in the user guide is embedded in the markdown and hence it is not easy to test. It would be nice to automatically test them. This JIRA is to discuss options to automate example code testing and see what we can do in Spark 1.6.

Goal is to move actual example code to spark/examples and test compilation in Jenkins builds. Then in the markdown, we can reference part of the code to show in the user guide. This requires adding a Jekyll tag that is similar to https://github.com/jekyll/jekyll/blob/master/lib/jekyll/tags/include.rb, e.g., called include_example.
`{% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %}`
Jekyll will find `examples/src/main/scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala` and pick code blocks marked "example" and replace code block in
`{% highlight %}`
 in the markdown.

See more sub-tasks in parent ticket: https://issues.apache.org/jira/browse/SPARK-11337

Author: Xin Ren <iamshrek@126.com>

Closes #11108 from keypointt/SPARK-13019.

18 files changed, 1020 insertions, 0 deletions

diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java
new file mode 100644
index 0000000000..fd19b43504
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java
@@ -0,0 +1,70 @@
+/*
+ * 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.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaDoubleRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Matrix;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.stat.Statistics;
+// $example off$
+
+public class JavaCorrelationsExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaCorrelationsExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaDoubleRDD seriesX = jsc.parallelizeDoubles(
+      Arrays.asList(1.0, 2.0, 3.0, 3.0, 5.0));  // a series
+
+    // must have the same number of partitions and cardinality as seriesX
+    JavaDoubleRDD seriesY = jsc.parallelizeDoubles(
+      Arrays.asList(11.0, 22.0, 33.0, 33.0, 555.0));
+
+    // compute the correlation using Pearson's method. Enter "spearman" for Spearman's method.
+    // If a method is not specified, Pearson's method will be used by default.
+    Double correlation = Statistics.corr(seriesX.srdd(), seriesY.srdd(), "pearson");
+    System.out.println("Correlation is: " + correlation);
+
+    // note that each Vector is a row and not a column
+    JavaRDD<Vector> data = jsc.parallelize(
+      Arrays.asList(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(5.0, 33.0, 366.0)
+      )
+    );
+
+    // calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method.
+    // If a method is not specified, Pearson's method will be used by default.
+    Matrix correlMatrix = Statistics.corr(data.rdd(), "pearson");
+    System.out.println(correlMatrix.toString());
+    // $example off$
+
+    jsc.stop();
+  }
+}
+
diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java
new file mode 100644
index 0000000000..b48b95ff1d
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java
@@ -0,0 +1,84 @@
+/*
+ * 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.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Matrices;
+import org.apache.spark.mllib.linalg.Matrix;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.stat.Statistics;
+import org.apache.spark.mllib.stat.test.ChiSqTestResult;
+// $example off$
+
+public class JavaHypothesisTestingExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaHypothesisTestingExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    // a vector composed of the frequencies of events
+    Vector vec = Vectors.dense(0.1, 0.15, 0.2, 0.3, 0.25);
+
+    // compute the goodness of fit. If a second vector to test against is not supplied
+    // as a parameter, the test runs against a uniform distribution.
+    ChiSqTestResult goodnessOfFitTestResult = Statistics.chiSqTest(vec);
+    // summary of the test including the p-value, degrees of freedom, test statistic,
+    // the method used, and the null hypothesis.
+    System.out.println(goodnessOfFitTestResult + "\n");
+
+    // Create a contingency matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
+    Matrix mat = Matrices.dense(3, 2, new double[]{1.0, 3.0, 5.0, 2.0, 4.0, 6.0});
+
+    // conduct Pearson's independence test on the input contingency matrix
+    ChiSqTestResult independenceTestResult = Statistics.chiSqTest(mat);
+    // summary of the test including the p-value, degrees of freedom...
+    System.out.println(independenceTestResult + "\n");
+
+    // an RDD of labeled points
+    JavaRDD<LabeledPoint> obs = jsc.parallelize(
+      Arrays.asList(
+        new LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0)),
+        new LabeledPoint(1.0, Vectors.dense(1.0, 2.0, 0.0)),
+        new LabeledPoint(-1.0, Vectors.dense(-1.0, 0.0, -0.5))
+      )
+    );
+
+    // The contingency table is constructed from the raw (feature, label) pairs and used to conduct
+    // the independence test. Returns an array containing the ChiSquaredTestResult for every feature
+    // against the label.
+    ChiSqTestResult[] featureTestResults = Statistics.chiSqTest(obs.rdd());
+    int i = 1;
+    for (ChiSqTestResult result : featureTestResults) {
+      System.out.println("Column " + i + ":");
+      System.out.println(result + "\n");  // summary of the test
+      i++;
+    }
+    // $example off$
+
+    jsc.stop();
+  }
+}
diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java
new file mode 100644
index 0000000000..fe611c9ae6
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java
@@ -0,0 +1,49 @@
+/*
+ * 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.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaDoubleRDD;
+import org.apache.spark.mllib.stat.Statistics;
+import org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult;
+// $example off$
+
+public class JavaHypothesisTestingKolmogorovSmirnovTestExample {
+  public static void main(String[] args) {
+
+    SparkConf conf =
+      new SparkConf().setAppName("JavaHypothesisTestingKolmogorovSmirnovTestExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaDoubleRDD data = jsc.parallelizeDoubles(Arrays.asList(0.1, 0.15, 0.2, 0.3, 0.25));
+    KolmogorovSmirnovTestResult testResult =
+      Statistics.kolmogorovSmirnovTest(data, "norm", 0.0, 1.0);
+    // summary of the test including the p-value, test statistic, and null hypothesis
+    // if our p-value indicates significance, we can reject the null hypothesis
+    System.out.println(testResult);
+    // $example off$
+
+    jsc.stop();
+  }
+}
+
diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java
new file mode 100644
index 0000000000..41de0d90ec
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java
@@ -0,0 +1,53 @@
+/*
+ * 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.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.stat.KernelDensity;
+// $example off$
+
+public class JavaKernelDensityEstimationExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaKernelDensityEstimationExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    // an RDD of sample data
+    JavaRDD<Double> data = jsc.parallelize(
+      Arrays.asList(1.0, 1.0, 1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 6.0, 7.0, 8.0, 9.0, 9.0));
+
+    // Construct the density estimator with the sample data
+    // and a standard deviation for the Gaussian kernels
+    KernelDensity kd = new KernelDensity().setSample(data).setBandwidth(3.0);
+
+    // Find density estimates for the given values
+    double[] densities = kd.estimate(new double[]{-1.0, 2.0, 5.0});
+
+    System.out.println(Arrays.toString(densities));
+    // $example off$
+
+    jsc.stop();
+  }
+}
+
diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java
new file mode 100644
index 0000000000..f5a451019b
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java
@@ -0,0 +1,75 @@
+/*
+ * 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.examples.mllib;
+
+import com.google.common.collect.ImmutableMap;
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+
+// $example on$
+import java.util.*;
+
+import scala.Tuple2;
+
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.function.VoidFunction;
+// $example off$
+
+public class JavaStratifiedSamplingExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaStratifiedSamplingExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    List<Tuple2<Integer, Character>> list = new ArrayList<Tuple2<Integer, Character>>(
+      Arrays.<Tuple2<Integer, Character>>asList(
+        new Tuple2(1, 'a'),
+        new Tuple2(1, 'b'),
+        new Tuple2(2, 'c'),
+        new Tuple2(2, 'd'),
+        new Tuple2(2, 'e'),
+        new Tuple2(3, 'f')
+      )
+    );
+
+    JavaPairRDD<Integer, Character> data = jsc.parallelizePairs(list);
+
+    // specify the exact fraction desired from each key Map<K, Object>
+    ImmutableMap<Integer, Object> fractions =
+      ImmutableMap.of(1, (Object)0.1, 2, (Object) 0.6, 3, (Object) 0.3);
+
+    // Get an approximate sample from each stratum
+    JavaPairRDD<Integer, Character> approxSample = data.sampleByKey(false, fractions);
+    // Get an exact sample from each stratum
+    JavaPairRDD<Integer, Character> exactSample = data.sampleByKeyExact(false, fractions);
+    // $example off$
+
+    System.out.println("approxSample size is " + approxSample.collect().size());
+    for (Tuple2<Integer, Character> t : approxSample.collect()) {
+      System.out.println(t._1() + " " + t._2());
+    }
+
+    System.out.println("exactSample size is " + exactSample.collect().size());
+    for (Tuple2<Integer, Character> t : exactSample.collect()) {
+      System.out.println(t._1() + " " + t._2());
+    }
+
+    jsc.stop();
+  }
+}
diff --git a/examples/src/main/java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java b/examples/src/main/java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java
new file mode 100644
index 0000000000..278706bc8f
--- /dev/null
+++ b/examples/src/main/java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java
@@ -0,0 +1,56 @@
+/*
+ * 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.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.stat.MultivariateStatisticalSummary;
+import org.apache.spark.mllib.stat.Statistics;
+// $example off$
+
+public class JavaSummaryStatisticsExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaSummaryStatisticsExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaRDD<Vector> mat = jsc.parallelize(
+      Arrays.asList(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(3.0, 30.0, 300.0)
+      )
+    ); // an RDD of Vectors
+
+    // Compute column summary statistics.
+    MultivariateStatisticalSummary summary = Statistics.colStats(mat.rdd());
+    System.out.println(summary.mean());  // a dense vector containing the mean value for each column
+    System.out.println(summary.variance());  // column-wise variance
+    System.out.println(summary.numNonzeros());  // number of nonzeros in each column
+    // $example off$
+
+    jsc.stop();
+  }
+}
diff --git a/examples/src/main/python/mllib/correlations_example.py b/examples/src/main/python/mllib/correlations_example.py
new file mode 100644
index 0000000000..66d18f6e5d
--- /dev/null
+++ b/examples/src/main/python/mllib/correlations_example.py
@@ -0,0 +1,48 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+import numpy as np
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="CorrelationsExample")  # SparkContext
+
+    # $example on$
+    seriesX = sc.parallelize([1.0, 2.0, 3.0, 3.0, 5.0])  # a series
+    # seriesY must have the same number of partitions and cardinality as seriesX
+    seriesY = sc.parallelize([11.0, 22.0, 33.0, 33.0, 555.0])
+
+    # Compute the correlation using Pearson's method. Enter "spearman" for Spearman's method.
+    # If a method is not specified, Pearson's method will be used by default.
+    print("Correlation is: " + str(Statistics.corr(seriesX, seriesY, method="pearson")))
+
+    data = sc.parallelize(
+        [np.array([1.0, 10.0, 100.0]), np.array([2.0, 20.0, 200.0]), np.array([5.0, 33.0, 366.0])]
+    )  # an RDD of Vectors
+
+    # calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method.
+    # If a method is not specified, Pearson's method will be used by default.
+    print(Statistics.corr(data, method="pearson"))
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/hypothesis_testing_example.py b/examples/src/main/python/mllib/hypothesis_testing_example.py
new file mode 100644
index 0000000000..e566ead0d3
--- /dev/null
+++ b/examples/src/main/python/mllib/hypothesis_testing_example.py
@@ -0,0 +1,65 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.linalg import Matrices, Vectors
+from pyspark.mllib.regression import LabeledPoint
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="HypothesisTestingExample")
+
+    # $example on$
+    vec = Vectors.dense(0.1, 0.15, 0.2, 0.3, 0.25)  # a vector composed of the frequencies of events
+
+    # compute the goodness of fit. If a second vector to test against
+    # is not supplied as a parameter, the test runs against a uniform distribution.
+    goodnessOfFitTestResult = Statistics.chiSqTest(vec)
+
+    # summary of the test including the p-value, degrees of freedom,
+    # test statistic, the method used, and the null hypothesis.
+    print("%s\n" % goodnessOfFitTestResult)
+
+    mat = Matrices.dense(3, 2, [1.0, 3.0, 5.0, 2.0, 4.0, 6.0])  # a contingency matrix
+
+    # conduct Pearson's independence test on the input contingency matrix
+    independenceTestResult = Statistics.chiSqTest(mat)
+
+    # summary of the test including the p-value, degrees of freedom,
+    # test statistic, the method used, and the null hypothesis.
+    print("%s\n" % independenceTestResult)
+
+    obs = sc.parallelize(
+        [LabeledPoint(1.0, [1.0, 0.0, 3.0]),
+         LabeledPoint(1.0, [1.0, 2.0, 0.0]),
+         LabeledPoint(1.0, [-1.0, 0.0, -0.5])]
+    )  # LabeledPoint(feature, label)
+
+    # The contingency table is constructed from an RDD of LabeledPoint and used to conduct
+    # the independence test. Returns an array containing the ChiSquaredTestResult for every feature
+    # against the label.
+    featureTestResults = Statistics.chiSqTest(obs)
+
+    for i, result in enumerate(featureTestResults):
+        print("Column %d:\n%s" % (i + 1, result))
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py b/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py
new file mode 100644
index 0000000000..ef380dee79
--- /dev/null
+++ b/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py
@@ -0,0 +1,40 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="HypothesisTestingKolmogorovSmirnovTestExample")
+
+    # $example on$
+    parallelData = sc.parallelize([0.1, 0.15, 0.2, 0.3, 0.25])
+
+    # run a KS test for the sample versus a standard normal distribution
+    testResult = Statistics.kolmogorovSmirnovTest(parallelData, "norm", 0, 1)
+    # summary of the test including the p-value, test statistic, and null hypothesis
+    # if our p-value indicates significance, we can reject the null hypothesis
+    # Note that the Scala functionality of calling Statistics.kolmogorovSmirnovTest with
+    # a lambda to calculate the CDF is not made available in the Python API
+    print(testResult)
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/kernel_density_estimation_example.py b/examples/src/main/python/mllib/kernel_density_estimation_example.py
new file mode 100644
index 0000000000..3e8f7241a4
--- /dev/null
+++ b/examples/src/main/python/mllib/kernel_density_estimation_example.py
@@ -0,0 +1,44 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import KernelDensity
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="KernelDensityEstimationExample")  # SparkContext
+
+    # $example on$
+    # an RDD of sample data
+    data = sc.parallelize([1.0, 1.0, 1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 6.0, 7.0, 8.0, 9.0, 9.0])
+
+    # Construct the density estimator with the sample data and a standard deviation for the Gaussian
+    # kernels
+    kd = KernelDensity()
+    kd.setSample(data)
+    kd.setBandwidth(3.0)
+
+    # Find density estimates for the given values
+    densities = kd.estimate([-1.0, 2.0, 5.0])
+    # $example off$
+
+    print(densities)
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/stratified_sampling_example.py b/examples/src/main/python/mllib/stratified_sampling_example.py
new file mode 100644
index 0000000000..a13f8f08dd
--- /dev/null
+++ b/examples/src/main/python/mllib/stratified_sampling_example.py
@@ -0,0 +1,38 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="StratifiedSamplingExample")  # SparkContext
+
+    # $example on$
+    # an RDD of any key value pairs
+    data = sc.parallelize([(1, 'a'), (1, 'b'), (2, 'c'), (2, 'd'), (2, 'e'), (3, 'f')])
+
+    # specify the exact fraction desired from each key as a dictionary
+    fractions = {1: 0.1, 2: 0.6, 3: 0.3}
+
+    approxSample = data.sampleByKey(False, fractions)
+    # $example off$
+
+    for each in approxSample.collect():
+        print(each)
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/summary_statistics_example.py b/examples/src/main/python/mllib/summary_statistics_example.py
new file mode 100644
index 0000000000..d55d1a2c2d
--- /dev/null
+++ b/examples/src/main/python/mllib/summary_statistics_example.py
@@ -0,0 +1,42 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+import numpy as np
+
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="SummaryStatisticsExample")  # SparkContext
+
+    # $example on$
+    mat = sc.parallelize(
+        [np.array([1.0, 10.0, 100.0]), np.array([2.0, 20.0, 200.0]), np.array([3.0, 30.0, 300.0])]
+    )  # an RDD of Vectors
+
+    # Compute column summary statistics.
+    summary = Statistics.colStats(mat)
+    print(summary.mean())  # a dense vector containing the mean value for each column
+    print(summary.variance())  # column-wise variance
+    print(summary.numNonzeros())  # number of nonzeros in each column
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/CorrelationsExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/CorrelationsExample.scala
new file mode 100644
index 0000000000..1202caf534
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/CorrelationsExample.scala
@@ -0,0 +1,62 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+// $example on$
+import org.apache.spark.mllib.linalg._
+import org.apache.spark.mllib.stat.Statistics
+import org.apache.spark.rdd.RDD
+// $example off$
+
+object CorrelationsExample {
+
+  def main(args: Array[String]): Unit = {
+
+    val conf = new SparkConf().setAppName("CorrelationsExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    val seriesX: RDD[Double] = sc.parallelize(Array(1, 2, 3, 3, 5))  // a series
+    // must have the same number of partitions and cardinality as seriesX
+    val seriesY: RDD[Double] = sc.parallelize(Array(11, 22, 33, 33, 555))
+
+    // compute the correlation using Pearson's method. Enter "spearman" for Spearman's method. If a
+    // method is not specified, Pearson's method will be used by default.
+    val correlation: Double = Statistics.corr(seriesX, seriesY, "pearson")
+    println(s"Correlation is: $correlation")
+
+    val data: RDD[Vector] = sc.parallelize(
+      Seq(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(5.0, 33.0, 366.0))
+    )  // note that each Vector is a row and not a column
+
+    // calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method
+    // If a method is not specified, Pearson's method will be used by default.
+    val correlMatrix: Matrix = Statistics.corr(data, "pearson")
+    println(correlMatrix.toString)
+    // $example off$
+
+    sc.stop()
+  }
+}
+// scalastyle:on println
+
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala
new file mode 100644
index 0000000000..0d391a3637
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala
@@ -0,0 +1,80 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+// $example on$
+import org.apache.spark.mllib.linalg._
+import org.apache.spark.mllib.regression.LabeledPoint
+import org.apache.spark.mllib.stat.Statistics
+import org.apache.spark.mllib.stat.test.ChiSqTestResult
+import org.apache.spark.rdd.RDD
+// $example off$
+
+object HypothesisTestingExample {
+
+  def main(args: Array[String]) {
+
+    val conf = new SparkConf().setAppName("HypothesisTestingExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    // a vector composed of the frequencies of events
+    val vec: Vector = Vectors.dense(0.1, 0.15, 0.2, 0.3, 0.25)
+
+    // compute the goodness of fit. If a second vector to test against is not supplied
+    // as a parameter, the test runs against a uniform distribution.
+    val goodnessOfFitTestResult = Statistics.chiSqTest(vec)
+    // summary of the test including the p-value, degrees of freedom, test statistic, the method
+    // used, and the null hypothesis.
+    println(s"$goodnessOfFitTestResult\n")
+
+    // a contingency matrix. Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
+    val mat: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
+
+    // conduct Pearson's independence test on the input contingency matrix
+    val independenceTestResult = Statistics.chiSqTest(mat)
+    // summary of the test including the p-value, degrees of freedom
+    println(s"$independenceTestResult\n")
+
+    val obs: RDD[LabeledPoint] =
+      sc.parallelize(
+        Seq(
+          LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0)),
+          LabeledPoint(1.0, Vectors.dense(1.0, 2.0, 0.0)),
+          LabeledPoint(-1.0, Vectors.dense(-1.0, 0.0, -0.5)
+          )
+        )
+      ) // (feature, label) pairs.
+
+    // The contingency table is constructed from the raw (feature, label) pairs and used to conduct
+    // the independence test. Returns an array containing the ChiSquaredTestResult for every feature
+    // against the label.
+    val featureTestResults: Array[ChiSqTestResult] = Statistics.chiSqTest(obs)
+    featureTestResults.zipWithIndex.foreach { case (k, v) =>
+      println("Column " + (v + 1).toString + ":")
+      println(k)
+    }  // summary of the test
+    // $example off$
+
+    sc.stop()
+  }
+}
+// scalastyle:on println
+
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala
new file mode 100644
index 0000000000..840874cf3c
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala
@@ -0,0 +1,54 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+// $example on$
+import org.apache.spark.mllib.stat.Statistics
+import org.apache.spark.rdd.RDD
+// $example off$
+
+object HypothesisTestingKolmogorovSmirnovTestExample {
+
+  def main(args: Array[String]): Unit = {
+
+    val conf = new SparkConf().setAppName("HypothesisTestingKolmogorovSmirnovTestExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    val data: RDD[Double] = sc.parallelize(Seq(0.1, 0.15, 0.2, 0.3, 0.25))  // an RDD of sample data
+
+    // run a KS test for the sample versus a standard normal distribution
+    val testResult = Statistics.kolmogorovSmirnovTest(data, "norm", 0, 1)
+    // summary of the test including the p-value, test statistic, and null hypothesis if our p-value
+    // indicates significance, we can reject the null hypothesis.
+    println(testResult)
+    println()
+
+    // perform a KS test using a cumulative distribution function of our making
+    val myCDF = Map(0.1 -> 0.2, 0.15 -> 0.6, 0.2 -> 0.05, 0.3 -> 0.05, 0.25 -> 0.1)
+    val testResult2 = Statistics.kolmogorovSmirnovTest(data, myCDF)
+    println(testResult2)
+    // $example off$
+
+    sc.stop()
+  }
+}
+// scalastyle:on println
+
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala
new file mode 100644
index 0000000000..cc5d159b36
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala
@@ -0,0 +1,54 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+// $example on$
+import org.apache.spark.mllib.stat.KernelDensity
+import org.apache.spark.rdd.RDD
+// $example off$
+
+object KernelDensityEstimationExample {
+
+  def main(args: Array[String]): Unit = {
+
+    val conf = new SparkConf().setAppName("KernelDensityEstimationExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    // an RDD of sample data
+    val data: RDD[Double] = sc.parallelize(Seq(1, 1, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9))
+
+    // Construct the density estimator with the sample data and a standard deviation
+    // for the Gaussian kernels
+    val kd = new KernelDensity()
+      .setSample(data)
+      .setBandwidth(3.0)
+
+    // Find density estimates for the given values
+    val densities = kd.estimate(Array(-1.0, 2.0, 5.0))
+    // $example off$
+
+    densities.foreach(println)
+
+    sc.stop()
+  }
+}
+// scalastyle:on println
+
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala
new file mode 100644
index 0000000000..169467926c
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala
@@ -0,0 +1,53 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+
+object StratifiedSamplingExample {
+
+  def main(args: Array[String]): Unit = {
+
+    val conf = new SparkConf().setAppName("StratifiedSamplingExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    // an RDD[(K, V)] of any key value pairs
+    val data = sc.parallelize(
+      Seq((1, 'a'), (1, 'b'), (2, 'c'), (2, 'd'), (2, 'e'), (3, 'f')))
+
+    // specify the exact fraction desired from each key
+    val fractions = Map(1 -> 0.1, 2 -> 0.6, 3 -> 0.3)
+
+    // Get an approximate sample from each stratum
+    val approxSample = data.sampleByKey(withReplacement = false, fractions)
+    // Get an exact sample from each stratum
+    val exactSample = data.sampleByKeyExact(withReplacement = false, fractions)
+    // $example off$
+
+    println("approxSample size is " + approxSample.collect().size.toString)
+    approxSample.collect().foreach(println)
+
+    println("exactSample its size is " + exactSample.collect().size.toString)
+    exactSample.collect().foreach(println)
+
+    sc.stop()
+  }
+}
+// scalastyle:on println
diff --git a/examples/src/main/scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala b/examples/src/main/scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala
new file mode 100644
index 0000000000..948b443c0a
--- /dev/null
+++ b/examples/src/main/scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala
@@ -0,0 +1,53 @@
+/*
+ * 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.
+ */
+
+// scalastyle:off println
+package org.apache.spark.examples.mllib
+
+import org.apache.spark.{SparkConf, SparkContext}
+// $example on$
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.stat.{MultivariateStatisticalSummary, Statistics}
+// $example off$
+
+object SummaryStatisticsExample {
+
+  def main(args: Array[String]): Unit = {
+
+    val conf = new SparkConf().setAppName("SummaryStatisticsExample")
+    val sc = new SparkContext(conf)
+
+    // $example on$
+    val observations = sc.parallelize(
+      Seq(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(3.0, 30.0, 300.0)
+      )
+    )
+
+    // Compute column summary statistics.
+    val summary: MultivariateStatisticalSummary = Statistics.colStats(observations)
+    println(summary.mean)  // a dense vector containing the mean value for each column
+    println(summary.variance)  // column-wise variance
+    println(summary.numNonzeros)  // number of nonzeros in each column
+    // $example off$
+
+    sc.stop()
+  }
+}
+// scalastyle:on println