[SPARK-20505][ML] Add docs and examples for ml.stat.Correlation and m…

…l.stat.ChiSquareTest.

## What changes were proposed in this pull request?
Add docs and examples for ```ml.stat.Correlation``` and ```ml.stat.ChiSquareTest```.

## How was this patch tested?
Generate docs and run examples manually, successfully.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #17994 from yanboliang/spark-20505.

docs/_data/menu-ml.yaml

@@ -1,3 +1,5 @@
+- text: Basic statistics
+  url: ml-statistics.html
 - text: Pipelines
   url: ml-pipeline.html
 - text: Extracting, transforming and selecting features

docs/ml-statistics.md

@@ -0,0 +1,92 @@
+---
+layout: global
+title: Basic Statistics
+displayTitle: Basic Statistics
+---
+
+
+`\[
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\]`
+
+**Table of Contents**
+
+* This will become a table of contents (this text will be scraped).
+{:toc}
+
+## Correlation
+
+Calculating the correlation between two series of data is a common operation in Statistics. In `spark.ml`
+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">
+[`Correlation`](api/scala/index.html#org.apache.spark.ml.stat.Correlation$)
+computes the correlation matrix for the input Dataset of Vectors using the specified method.
+The output will be a DataFrame that contains the correlation matrix of the column of vectors.
+
+{% include_example scala/org/apache/spark/examples/ml/CorrelationExample.scala %}
+</div>
+
+<div data-lang="java" markdown="1">
+[`Correlation`](api/java/org/apache/spark/ml/stat/Correlation.html)
+computes the correlation matrix for the input Dataset of Vectors using the specified method.
+The output will be a DataFrame that contains the correlation matrix of the column of vectors.
+
+{% include_example java/org/apache/spark/examples/ml/JavaCorrelationExample.java %}
+</div>
+
+<div data-lang="python" markdown="1">
+[`Correlation`](api/python/pyspark.ml.html#pyspark.ml.stat.Correlation$)
+computes the correlation matrix for the input Dataset of Vectors using the specified method.
+The output will be a DataFrame that contains the correlation matrix of the column of vectors.
+
+{% include_example python/ml/correlation_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.ml` currently supports Pearson's
+Chi-squared ( $\chi^2$) tests for independence.
+
+`ChiSquareTest` conducts Pearson's independence test for every feature against the label.
+For each feature, the (feature, label) pairs are converted into a contingency matrix for which
+the Chi-squared statistic is computed. All label and feature values must be categorical.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+Refer to the [`ChiSquareTest` Scala docs](api/scala/index.html#org.apache.spark.ml.stat.ChiSquareTest$) for details on the API.
+
+{% include_example scala/org/apache/spark/examples/ml/ChiSquareTestExample.scala %}
+</div>
+
+<div data-lang="java" markdown="1">
+Refer to the [`ChiSquareTest` Java docs](api/java/org/apache/spark/ml/stat/ChiSquareTest.html) for details on the API.
+
+{% include_example java/org/apache/spark/examples/ml/JavaChiSquareTestExample.java %}
+</div>
+
+<div data-lang="python" markdown="1">
+Refer to the [`ChiSquareTest` Python docs](api/python/index.html#pyspark.ml.stat.ChiSquareTest$) for details on the API.
+
+{% include_example python/ml/chi_square_test_example.py %}
+</div>
+
+</div>

examples/src/main/java/org/apache/spark/examples/ml/JavaChiSquareTestExample.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.ml;
+
+import org.apache.spark.sql.SparkSession;
+
+// $example on$
+import java.util.Arrays;
+import java.util.List;
+
+import org.apache.spark.ml.linalg.Vectors;
+import org.apache.spark.ml.linalg.VectorUDT;
+import org.apache.spark.ml.stat.ChiSquareTest;
+import org.apache.spark.sql.Dataset;
+import org.apache.spark.sql.Row;
+import org.apache.spark.sql.RowFactory;
+import org.apache.spark.sql.types.*;
+// $example off$
+
+/**
+ * An example for Chi-square hypothesis testing.
+ * Run with
+ * <pre>
+ * bin/run-example ml.JavaChiSquareTestExample
+ * </pre>
+ */
+public class JavaChiSquareTestExample {
+
+  public static void main(String[] args) {
+    SparkSession spark = SparkSession
+      .builder()
+      .appName("JavaChiSquareTestExample")
+      .getOrCreate();
+
+    // $example on$
+    List<Row> data = Arrays.asList(
+      RowFactory.create(0.0, Vectors.dense(0.5, 10.0)),
+      RowFactory.create(0.0, Vectors.dense(1.5, 20.0)),
+      RowFactory.create(1.0, Vectors.dense(1.5, 30.0)),
+      RowFactory.create(0.0, Vectors.dense(3.5, 30.0)),
+      RowFactory.create(0.0, Vectors.dense(3.5, 40.0)),
+      RowFactory.create(1.0, Vectors.dense(3.5, 40.0))
+    );
+
+    StructType schema = new StructType(new StructField[]{
+      new StructField("label", DataTypes.DoubleType, false, Metadata.empty()),
+      new StructField("features", new VectorUDT(), false, Metadata.empty()),
+    });
+
+    Dataset<Row> df = spark.createDataFrame(data, schema);
+    Row r = ChiSquareTest.test(df, "features", "label").head();
+    System.out.println("pValues: " + r.get(0).toString());
+    System.out.println("degreesOfFreedom: " + r.getList(1).toString());
+    System.out.println("statistics: " + r.get(2).toString());
+
+    // $example off$
+
+    spark.stop();
+  }
+}

examples/src/main/java/org/apache/spark/examples/ml/JavaCorrelationExample.java

@@ -0,0 +1,72 @@
+/*
+ * 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.ml;
+
+import org.apache.spark.sql.SparkSession;
+
+// $example on$
+import java.util.Arrays;
+import java.util.List;
+
+import org.apache.spark.ml.linalg.Vectors;
+import org.apache.spark.ml.linalg.VectorUDT;
+import org.apache.spark.ml.stat.Correlation;
+import org.apache.spark.sql.Dataset;
+import org.apache.spark.sql.Row;
+import org.apache.spark.sql.RowFactory;
+import org.apache.spark.sql.types.*;
+// $example off$
+
+/**
+ * An example for computing correlation matrix.
+ * Run with
+ * <pre>
+ * bin/run-example ml.JavaCorrelationExample
+ * </pre>
+ */
+public class JavaCorrelationExample {
+
+  public static void main(String[] args) {
+    SparkSession spark = SparkSession
+      .builder()
+      .appName("JavaCorrelationExample")
+      .getOrCreate();
+
+    // $example on$
+    List<Row> data = Arrays.asList(
+      RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{1.0, -2.0})),
+      RowFactory.create(Vectors.dense(4.0, 5.0, 0.0, 3.0)),
+      RowFactory.create(Vectors.dense(6.0, 7.0, 0.0, 8.0)),
+      RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{9.0, 1.0}))
+    );
+
+    StructType schema = new StructType(new StructField[]{
+      new StructField("features", new VectorUDT(), false, Metadata.empty()),
+    });
+
+    Dataset<Row> df = spark.createDataFrame(data, schema);
+    Row r1 = Correlation.corr(df, "features").head();
+    System.out.println("Pearson correlation matrix:\n" + r1.get(0).toString());
+
+    Row r2 = Correlation.corr(df, "features", "spearman").head();
+    System.out.println("Spearman correlation matrix:\n" + r2.get(0).toString());
+    // $example off$
+
+    spark.stop();
+  }
+}

examples/src/main/python/ml/chi_square_test_example.py

@@ -0,0 +1,52 @@
+#
+# 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.sql import SparkSession
+# $example on$
+from pyspark.ml.linalg import Vectors
+from pyspark.ml.stat import ChiSquareTest
+# $example off$
+
+"""
+An example for Chi-square hypothesis testing.
+Run with:
+  bin/spark-submit examples/src/main/python/ml/chi_square_test_example.py
+"""
+if __name__ == "__main__":
+    spark = SparkSession \
+        .builder \
+        .appName("ChiSquareTestExample") \
+        .getOrCreate()
+
+    # $example on$
+    data = [(0.0, Vectors.dense(0.5, 10.0)),
+            (0.0, Vectors.dense(1.5, 20.0)),
+            (1.0, Vectors.dense(1.5, 30.0)),
+            (0.0, Vectors.dense(3.5, 30.0)),
+            (0.0, Vectors.dense(3.5, 40.0)),
+            (1.0, Vectors.dense(3.5, 40.0))]
+    df = spark.createDataFrame(data, ["label", "features"])
+
+    r = ChiSquareTest.test(df, "features", "label").head()
+    print("pValues: " + str(r.pValues))
+    print("degreesOfFreedom: " + str(r.degreesOfFreedom))
+    print("statistics: " + str(r.statistics))
+    # $example off$
+
+    spark.stop()

examples/src/main/python/ml/correlation_example.py

@@ -0,0 +1,51 @@
+#
+# 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
+
+# $example on$
+from pyspark.ml.linalg import Vectors
+from pyspark.ml.stat import Correlation
+# $example off$
+from pyspark.sql import SparkSession
+
+"""
+An example for computing correlation matrix.
+Run with:
+  bin/spark-submit examples/src/main/python/ml/correlation_example.py
+"""
+if __name__ == "__main__":
+    spark = SparkSession \
+        .builder \
+        .appName("CorrelationExample") \
+        .getOrCreate()
+
+    # $example on$
+    data = [(Vectors.sparse(4, [(0, 1.0), (3, -2.0)]),),
+            (Vectors.dense([4.0, 5.0, 0.0, 3.0]),),
+            (Vectors.dense([6.0, 7.0, 0.0, 8.0]),),
+            (Vectors.sparse(4, [(0, 9.0), (3, 1.0)]),)]
+    df = spark.createDataFrame(data, ["features"])
+
+    r1 = Correlation.corr(df, "features").head()
+    print("Pearson correlation matrix:\n" + str(r1[0]))
+
+    r2 = Correlation.corr(df, "features", "spearman").head()
+    print("Spearman correlation matrix:\n" + str(r2[0]))
+    # $example off$
+
+    spark.stop()