Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/2123#discussion_r16695707
--- Diff: docs/mllib-stats.md ---
@@ -99,69 +99,336 @@ v = u.map(lambda x: 1.0 + 2.0 * x)
</div>
-## Stratified Sampling
+## Correlation Calculation
+
+Calculating the correlation between two series of data is a common
operation in Statistics. In MLlib
+we provide the flexibility to calculate correlation between 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
+an `RDD[Vector]`, the output will be a `Double` or the correlation
`Matrix` respectively.
+
+{% 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 %}
+</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
+a `JavaRDD<Vector>`, the output will be a `Double` or the correlation
`Matrix` respectively.
+
+{% 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 %}
+</div>
+
+<div data-lang="python" markdown="1">
+[`Statistics`](api/python/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.
+
+Support for `RowMatrix` operations in python currently don't exist, but
will be added in future
+releases.
+
+{% 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 %}
+</div>
+
+</div>
+
+## Stratified Sampling
+
+Unlike the other statistics functions, which reside in MLLib, stratified
sampling methods,
+`sampleByKey` and `sampleByKeyExact`, can be accessed in
`PairRDDFunctions` in core, as stratified
+sampling is tightly coupled with the PairRDD data type, and the function
signature conforms to the
+other *ByKey* methods in PairRDDFunctions. A separate method for exact
sample size support exists
+as it requires significant more resources than the per-stratum simple
random sampling used in
+`sampleByKey`.
+
+<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
+fraction for key $k$, and $n_k$ is the number of key-value pairs for key
$k$.
+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.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 sample = data.sampleByKeyExact(withReplacement=false, fractions)
--- End diff --
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