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

layout	title	displayTitle
global	Basic Statistics	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.

[`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 %}

[`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 %}

[`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 %}

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.

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 %}

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 %}

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 %}

Summarizer

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

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 %}

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 %}

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 %}