spark-instrumented-optimizer/docs/ml-statistics.md

---
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title: Basic Statistics
displayTitle: Basic Statistics
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**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>

## Summarizer

We provide vector column summary statistics for `Dataframe` through `Summarizer`.
Available metrics are the column-wise max, min, mean, sum, variance, std, and number of nonzeros,
as well as the total count.

<div class="codetabs">
<div data-lang="scala" markdown="1">
The following example demonstrates using [`Summarizer`](api/scala/index.html#org.apache.spark.ml.stat.Summarizer$)
to compute the mean and variance for a vector column of the input dataframe, with and without a weight column.

{% include_example scala/org/apache/spark/examples/ml/SummarizerExample.scala %}
</div>

<div data-lang="java" markdown="1">
The following example demonstrates using [`Summarizer`](api/java/org/apache/spark/ml/stat/Summarizer.html)
to compute the mean and variance for a vector column of the input dataframe, with and without a weight column.

{% include_example java/org/apache/spark/examples/ml/JavaSummarizerExample.java %}
</div>

<div data-lang="python" markdown="1">
Refer to the [`Summarizer` Python docs](api/python/index.html#pyspark.ml.stat.Summarizer$) for details on the API.

{% include_example python/ml/summarizer_example.py %}
</div>

</div>