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diff --git a/docs/mllib-stats.md b/docs/mllib-stats.md new file mode 100644 index 0000000000..ca9ef46c15 --- /dev/null +++ b/docs/mllib-stats.md @@ -0,0 +1,95 @@ +--- +layout: global +title: Statistics Functionality - MLlib +displayTitle: <a href="mllib-guide.html">MLlib</a> - Statistics Functionality +--- + +* Table of contents +{:toc} + + +`\[ +\newcommand{\R}{\mathbb{R}} +\newcommand{\E}{\mathbb{E}} +\newcommand{\x}{\mathbf{x}} +\newcommand{\y}{\mathbf{y}} +\newcommand{\wv}{\mathbf{w}} +\newcommand{\av}{\mathbf{\alpha}} +\newcommand{\bv}{\mathbf{b}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\id}{\mathbf{I}} +\newcommand{\ind}{\mathbf{1}} +\newcommand{\0}{\mathbf{0}} +\newcommand{\unit}{\mathbf{e}} +\newcommand{\one}{\mathbf{1}} +\newcommand{\zero}{\mathbf{0}} +\]` + +## Data Generators + +## Stratified Sampling + +## Summary Statistics + +### Multivariate summary statistics + +We provide column summary statistics for `RowMatrix` (note: this functionality is not currently supported in `IndexedRowMatrix` or `CoordinateMatrix`). +If the number of columns is not large, e.g., on the order of thousands, then the +covariance matrix can also be computed as a local matrix, which requires $\mathcal{O}(n^2)$ storage where $n$ is the +number of columns. The total CPU time is $\mathcal{O}(m n^2)$, where $m$ is the number of rows, +and is faster if the rows are sparse. + +<div class="codetabs"> +<div data-lang="scala" markdown="1"> + +[`computeColumnSummaryStatistics()`](api/scala/index.html#org.apache.spark.mllib.linalg.distributed.RowMatrix) returns an instance of +[`MultivariateStatisticalSummary`](api/scala/index.html#org.apache.spark.mllib.stat.MultivariateStatisticalSummary), +which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the +total count. + +{% highlight scala %} +import org.apache.spark.mllib.linalg.Matrix +import org.apache.spark.mllib.linalg.distributed.RowMatrix +import org.apache.spark.mllib.stat.MultivariateStatisticalSummary + +val mat: RowMatrix = ... // a RowMatrix + +// Compute column summary statistics. +val summary: MultivariateStatisticalSummary = mat.computeColumnSummaryStatistics() +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 + +// Compute the covariance matrix. +val cov: Matrix = mat.computeCovariance() +{% endhighlight %} +</div> + +<div data-lang="java" markdown="1"> + +[`RowMatrix#computeColumnSummaryStatistics`](api/java/org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computeColumnSummaryStatistics()) returns an instance of +[`MultivariateStatisticalSummary`](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html), +which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the +total count. + +{% highlight java %} +import org.apache.spark.mllib.linalg.Matrix; +import org.apache.spark.mllib.linalg.distributed.RowMatrix; +import org.apache.spark.mllib.stat.MultivariateStatisticalSummary; + +RowMatrix mat = ... // a RowMatrix + +// Compute column summary statistics. +MultivariateStatisticalSummary summary = mat.computeColumnSummaryStatistics(); +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 + +// Compute the covariance matrix. +Matrix cov = mat.computeCovariance(); +{% endhighlight %} +</div> +</div> + + +## Hypothesis Testing |