[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.

1 files changed, 56 insertions, 382 deletions

diff --git a/docs/mllib-statistics.md b/docs/mllib-statistics.md
index b773031bc7..02b81f153b 100644
--- a/docs/mllib-statistics.md
+++ b/docs/mllib-statistics.md
@@ -10,24 +10,24 @@ displayTitle: Basic Statistics - spark.mllib
 
 `\[
 \newcommand{\R}{\mathbb{R}}
-\newcommand{\E}{\mathbb{E}} 
+\newcommand{\E}{\mathbb{E}}
 \newcommand{\x}{\mathbf{x}}
 \newcommand{\y}{\mathbf{y}}
 \newcommand{\wv}{\mathbf{w}}
 \newcommand{\av}{\mathbf{\alpha}}
 \newcommand{\bv}{\mathbf{b}}
 \newcommand{\N}{\mathbb{N}}
-\newcommand{\id}{\mathbf{I}} 
-\newcommand{\ind}{\mathbf{1}} 
-\newcommand{\0}{\mathbf{0}} 
-\newcommand{\unit}{\mathbf{e}} 
-\newcommand{\one}{\mathbf{1}} 
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
 \newcommand{\zero}{\mathbf{0}}
 \]`
 
-## Summary statistics 
+## Summary statistics
 
-We provide column summary statistics for `RDD[Vector]` through the function `colStats` 
+We provide column summary statistics for `RDD[Vector]` through the function `colStats`
 available in `Statistics`.
 
 <div class="codetabs">
@@ -40,19 +40,7 @@ total count.
 
 Refer to the [`MultivariateStatisticalSummary` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.MultivariateStatisticalSummary) for details on the API.
 
-{% highlight scala %}
-import org.apache.spark.mllib.linalg.Vector
-import org.apache.spark.mllib.stat.{MultivariateStatisticalSummary, Statistics}
-
-val observations: RDD[Vector] = ... // an RDD of Vectors
-
-// 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
-
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
@@ -64,24 +52,7 @@ total count.
 
 Refer to the [`MultivariateStatisticalSummary` Java docs](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html) for details on the API.
 
-{% highlight java %}
-import org.apache.spark.api.java.JavaRDD;
-import org.apache.spark.api.java.JavaSparkContext;
-import org.apache.spark.mllib.linalg.Vector;
-import org.apache.spark.mllib.stat.MultivariateStatisticalSummary;
-import org.apache.spark.mllib.stat.Statistics;
-
-JavaSparkContext jsc = ...
-
-JavaRDD<Vector> mat = ... // 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
-
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
@@ -92,20 +63,7 @@ total count.
 
 Refer to the [`MultivariateStatisticalSummary` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary) for more details on the API.
 
-{% highlight python %}
-from pyspark.mllib.stat import Statistics
-
-sc = ... # SparkContext
-
-mat = ... # an RDD of Vectors
-
-# Compute column summary statistics.
-summary = Statistics.colStats(mat)
-print(summary.mean())
-print(summary.variance())
-print(summary.numNonzeros())
-
-{% endhighlight %}
+{% include_example python/mllib/summary_statistics_example.py %}
 </div>
 
 </div>
@@ -113,96 +71,38 @@ print(summary.numNonzeros())
 ## Correlations
 
 Calculating the correlation between two series of data is a common operation in Statistics. In `spark.mllib`
-we provide the flexibility to calculate pairwise correlations among many series. The supported 
+we provide the flexibility to calculate pairwise correlations among many series. The supported
 correlation methods are currently Pearson's and Spearman's correlation.
- 
+
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
-[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to 
-calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or 
+[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to
+calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
 an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.Statistics) for details on the API.
 
-{% highlight scala %}
-import org.apache.spark.SparkContext
-import org.apache.spark.mllib.linalg._
-import org.apache.spark.mllib.stat.Statistics
-
-val sc: SparkContext = ...
-
-val seriesX: RDD[Double] = ... // a series
-val seriesY: RDD[Double] = ... // must have the same number of partitions and cardinality as seriesX
-
-// 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")
-
-val data: RDD[Vector] = ... // 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")
-
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/CorrelationsExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
-[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to 
-calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or 
+[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
+calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or
 a `JavaRDD<Vector>`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
 
-{% highlight java %}
-import org.apache.spark.api.java.JavaDoubleRDD;
-import org.apache.spark.api.java.JavaSparkContext;
-import org.apache.spark.mllib.linalg.*;
-import org.apache.spark.mllib.stat.Statistics;
-
-JavaSparkContext jsc = ...
-
-JavaDoubleRDD seriesX = ... // a series
-JavaDoubleRDD seriesY = ... // must have the same number of partitions and cardinality as seriesX
-
-// 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");
-
-JavaRDD<Vector> data = ... // 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. 
-Matrix correlMatrix = Statistics.corr(data.rdd(), "pearson");
-
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
-[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to 
-calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or 
+[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to
+calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
 an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
-{% highlight python %}
-from pyspark.mllib.stat import Statistics
-
-sc = ... # SparkContext
-
-seriesX = ... # a series
-seriesY = ... # must have the same number of partitions and cardinality as seriesX
-
-# 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(Statistics.corr(seriesX, seriesY, method="pearson"))
-
-data = ... # 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"))
-
-{% endhighlight %}
+{% include_example python/mllib/correlations_example.py %}
 </div>
 
 </div>
@@ -211,187 +111,76 @@ print(Statistics.corr(data, method="pearson"))
 
 Unlike the other statistics functions, which reside in `spark.mllib`, stratified sampling methods,
 `sampleByKey` and `sampleByKeyExact`, can be performed on RDD's of key-value pairs. For stratified
-sampling, the keys can be thought of as a label and the value as a specific attribute. For example 
-the key can be man or woman, or document ids, and the respective values can be the list of ages 
-of the people in the population or the list of words in the documents. The `sampleByKey` method 
-will flip a coin to decide whether an observation will be sampled or not, therefore requires one 
-pass over the data, and provides an *expected* sample size. `sampleByKeyExact` requires significant 
+sampling, the keys can be thought of as a label and the value as a specific attribute. For example
+the key can be man or woman, or document ids, and the respective values can be the list of ages
+of the people in the population or the list of words in the documents. The `sampleByKey` method
+will flip a coin to decide whether an observation will be sampled or not, therefore requires one
+pass over the data, and provides an *expected* sample size. `sampleByKeyExact` requires significant
 more resources than the per-stratum simple random sampling used in `sampleByKey`, but will provide
-the exact sampling size with 99.99% confidence. `sampleByKeyExact` is currently not supported in 
+the exact sampling size with 99.99% confidence. `sampleByKeyExact` is currently not supported in
 python.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`sampleByKeyExact()`](api/scala/index.html#org.apache.spark.rdd.PairRDDFunctions) allows users to
-sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired 
+sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
 fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
-keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample 
+keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
 size, whereas sampling with replacement requires two additional passes.
 
-{% highlight scala %}
-import org.apache.spark.SparkContext
-import org.apache.spark.SparkContext._
-import org.apache.spark.rdd.PairRDDFunctions
-
-val sc: SparkContext = ...
-
-val data = ... // an RDD[(K, V)] of any key value pairs
-val fractions: Map[K, Double] = ... // specify the exact fraction desired from each key
-
-// Get an exact sample from each stratum
-val approxSample = data.sampleByKey(withReplacement = false, fractions)
-val exactSample = data.sampleByKeyExact(withReplacement = false, fractions)
-
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`sampleByKeyExact()`](api/java/org/apache/spark/api/java/JavaPairRDD.html) allows users to
-sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired 
+sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
 fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
-keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample 
+keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
 size, whereas sampling with replacement requires two additional passes.
 
-{% highlight java %}
-import java.util.Map;
-
-import org.apache.spark.api.java.JavaPairRDD;
-import org.apache.spark.api.java.JavaSparkContext;
-
-JavaSparkContext jsc = ...
-
-JavaPairRDD<K, V> data = ... // an RDD of any key value pairs
-Map<K, Object> fractions = ... // specify the exact fraction desired from each key
-
-// Get an exact sample from each stratum
-JavaPairRDD<K, V> approxSample = data.sampleByKey(false, fractions);
-JavaPairRDD<K, V> exactSample = data.sampleByKeyExact(false, fractions);
-
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java %}
 </div>
 <div data-lang="python" markdown="1">
 [`sampleByKey()`](api/python/pyspark.html#pyspark.RDD.sampleByKey) allows users to
-sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the 
-desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the 
+sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the
+desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the
 set of keys.
 
 *Note:* `sampleByKeyExact()` is currently not supported in Python.
 
-{% highlight python %}
-
-sc = ... # SparkContext
-
-data = ... # an RDD of any key value pairs
-fractions = ... # specify the exact fraction desired from each key as a dictionary
-
-approxSample = data.sampleByKey(False, fractions);
-
-{% endhighlight %}
+{% include_example python/mllib/stratified_sampling_example.py %}
 </div>
 
 </div>
 
 ## Hypothesis testing
 
-Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically 
-significant, whether this result occurred by chance or not. `spark.mllib` currently supports Pearson's 
+Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically
+significant, whether this result occurred by chance or not. `spark.mllib` currently supports Pearson's
 chi-squared ( $\chi^2$) tests for goodness of fit and independence. The input data types determine
-whether the goodness of fit or the independence test is conducted. The goodness of fit test requires 
+whether the goodness of fit or the independence test is conducted. The goodness of fit test requires
 an input type of `Vector`, whereas the independence test requires a `Matrix` as input.
 
-`spark.mllib` also supports the input type `RDD[LabeledPoint]` to enable feature selection via chi-squared 
+`spark.mllib` also supports the input type `RDD[LabeledPoint]` to enable feature selection via chi-squared
 independence tests.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
-[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to 
-run Pearson's chi-squared tests. The following example demonstrates how to run and interpret 
+[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to
+run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
 hypothesis tests.
 
-{% highlight scala %}
-import org.apache.spark.SparkContext
-import org.apache.spark.mllib.linalg._
-import org.apache.spark.mllib.regression.LabeledPoint
-import org.apache.spark.mllib.stat.Statistics._
-
-val sc: SparkContext = ...
-
-val vec: Vector = ... // 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.  
-val goodnessOfFitTestResult = Statistics.chiSqTest(vec)
-println(goodnessOfFitTestResult) // summary of the test including the p-value, degrees of freedom, 
-                                 // test statistic, the method used, and the null hypothesis.
-
-val mat: Matrix = ... // a contingency matrix
-
-// conduct Pearson's independence test on the input contingency matrix
-val independenceTestResult = Statistics.chiSqTest(mat) 
-println(independenceTestResult) // summary of the test including the p-value, degrees of freedom...
-
-val obs: RDD[LabeledPoint] = ... // (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)
-var i = 1
-featureTestResults.foreach { result =>
-    println(s"Column $i:\n$result")
-    i += 1
-} // summary of the test 
-
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
-[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to 
-run Pearson's chi-squared tests. The following example demonstrates how to run and interpret 
+[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
+run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
 hypothesis tests.
 
 Refer to the [`ChiSqTestResult` Java docs](api/java/org/apache/spark/mllib/stat/test/ChiSqTestResult.html) for details on the API.
 
-{% highlight java %}
-import org.apache.spark.api.java.JavaRDD;
-import org.apache.spark.api.java.JavaSparkContext;
-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;
-
-JavaSparkContext jsc = ...
-
-Vector vec = ... // 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.  
-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);
-
-Matrix mat = ... // a contingency matrix
-
-// 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);
-
-JavaRDD<LabeledPoint> obs = ... // an RDD of labeled points
-
-// 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); // summary of the test
-    i++;
-}
-
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
@@ -401,50 +190,18 @@ hypothesis tests.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
-{% highlight python %}
-from pyspark import SparkContext
-from pyspark.mllib.linalg import Vectors, Matrices
-from pyspark.mllib.regresssion import LabeledPoint
-from pyspark.mllib.stat import Statistics
-
-sc = SparkContext()
-
-vec = Vectors.dense(...) # 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)
-print(goodnessOfFitTestResult) # summary of the test including the p-value, degrees of freedom,
-                               # test statistic, the method used, and the null hypothesis.
-
-mat = Matrices.dense(...) # a contingency matrix
-
-# conduct Pearson's independence test on the input contingency matrix
-independenceTestResult = Statistics.chiSqTest(mat)
-print(independenceTestResult)  # summary of the test including the p-value, degrees of freedom...
-
-obs = sc.parallelize(...)  # 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:" % (i + 1))
-    print(result)
-{% endhighlight %}
+{% include_example python/mllib/hypothesis_testing_example.py %}
 </div>
 
 </div>
 
 Additionally, `spark.mllib` provides a 1-sample, 2-sided implementation of the Kolmogorov-Smirnov (KS) test
 for equality of probability distributions. By providing the name of a theoretical distribution
-(currently solely supported for the normal distribution) and its parameters, or a function to 
+(currently solely supported for the normal distribution) and its parameters, or a function to
 calculate the cumulative distribution according to a given theoretical distribution, the user can
 test the null hypothesis that their sample is drawn from that distribution. In the case that the
 user tests against the normal distribution (`distName="norm"`), but does not provide distribution
-parameters, the test initializes to the standard normal distribution and logs an appropriate 
+parameters, the test initializes to the standard normal distribution and logs an appropriate
 message.
 
 <div class="codetabs">
@@ -455,21 +212,7 @@ and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.Statistics) for details on the API.
 
-{% highlight scala %}
-import org.apache.spark.mllib.stat.Statistics
-
-val data: RDD[Double] = ... // 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)
-println(testResult) // 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
-
-// perform a KS test using a cumulative distribution function of our making
-val myCDF: Double => Double = ...
-val testResult2 = Statistics.kolmogorovSmirnovTest(data, myCDF)
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
@@ -479,23 +222,7 @@ and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
 
-{% highlight java %}
-import java.util.Arrays;
-
-import org.apache.spark.api.java.JavaDoubleRDD;
-import org.apache.spark.api.java.JavaSparkContext;
-
-import org.apache.spark.mllib.stat.Statistics;
-import org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult;
-
-JavaSparkContext jsc = ...
-JavaDoubleRDD data = jsc.parallelizeDoubles(Arrays.asList(0.2, 1.0, ...));
-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);
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
@@ -505,19 +232,7 @@ and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
-{% highlight python %}
-from pyspark.mllib.stat import Statistics
-
-parallelData = sc.parallelize([1.0, 2.0, ... ])
-
-# run a KS test for the sample versus a standard normal distribution
-testResult = Statistics.kolmogorovSmirnovTest(parallelData, "norm", 0, 1)
-print(testResult) # 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
-{% endhighlight %}
+{% include_example python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py %}
 </div>
 </div>
 
@@ -651,21 +366,7 @@ to do so.
 
 Refer to the [`KernelDensity` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.KernelDensity) for details on the API.
 
-{% highlight scala %}
-import org.apache.spark.mllib.stat.KernelDensity
-import org.apache.spark.rdd.RDD
-
-val data: RDD[Double] = ... // an RDD of sample data
-
-// 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))
-{% endhighlight %}
+{% include_example scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
@@ -675,21 +376,7 @@ to do so.
 
 Refer to the [`KernelDensity` Java docs](api/java/org/apache/spark/mllib/stat/KernelDensity.html) for details on the API.
 
-{% highlight java %}
-import org.apache.spark.mllib.stat.KernelDensity;
-import org.apache.spark.rdd.RDD;
-
-RDD<Double> data = ... // an RDD of sample data
-
-// 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});
-{% endhighlight %}
+{% include_example java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
@@ -699,20 +386,7 @@ to do so.
 
 Refer to the [`KernelDensity` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) for more details on the API.
 
-{% highlight python %}
-from pyspark.mllib.stat import KernelDensity
-
-data = ... # an RDD of sample data
-
-# 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])
-{% endhighlight %}
+{% include_example python/mllib/kernel_density_estimation_example.py %}
 </div>
 
 </div>