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| <h1 class="title">Basic Statistics - RDD-based API</h1> |
| |
| |
| <ul id="markdown-toc"> |
| <li><a href="#summary-statistics" id="markdown-toc-summary-statistics">Summary statistics</a></li> |
| <li><a href="#correlations" id="markdown-toc-correlations">Correlations</a></li> |
| <li><a href="#stratified-sampling" id="markdown-toc-stratified-sampling">Stratified sampling</a></li> |
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| </ul> |
| |
| <p><code class="language-plaintext highlighter-rouge">\[ |
| \newcommand{\R}{\mathbb{R}} |
| \newcommand{\E}{\mathbb{E}} |
| \newcommand{\x}{\mathbf{x}} |
| \newcommand{\y}{\mathbf{y}} |
| \newcommand{\wv}{\mathbf{w}} |
| \newcommand{\av}{\mathbf{\alpha}} |
| \newcommand{\bv}{\mathbf{b}} |
| \newcommand{\N}{\mathbb{N}} |
| \newcommand{\id}{\mathbf{I}} |
| \newcommand{\ind}{\mathbf{1}} |
| \newcommand{\0}{\mathbf{0}} |
| \newcommand{\unit}{\mathbf{e}} |
| \newcommand{\one}{\mathbf{1}} |
| \newcommand{\zero}{\mathbf{0}} |
| \]</code></p> |
| |
| <h2 id="summary-statistics">Summary statistics</h2> |
| |
| <p>We provide column summary statistics for <code class="language-plaintext highlighter-rouge">RDD[Vector]</code> through the function <code class="language-plaintext highlighter-rouge">colStats</code> |
| available in <code class="language-plaintext highlighter-rouge">Statistics</code>.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html#pyspark.mllib.stat.Statistics.colStats"><code class="language-plaintext highlighter-rouge">colStats()</code></a> returns an instance of |
| <a href="api/python/reference/api/pyspark.mllib.stat.MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code></a>, |
| which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the |
| total count.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.stat.MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="n">np</span> |
| |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.stat</span> <span class="kn">import</span> <span class="n">Statistics</span> |
| |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">(</span> |
| <span class="p">[</span><span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="mf">100.0</span><span class="p">]),</span> <span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">20.0</span><span class="p">,</span> <span class="mf">200.0</span><span class="p">]),</span> <span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">30.0</span><span class="p">,</span> <span class="mf">300.0</span><span class="p">])]</span> |
| <span class="p">)</span> <span class="c1"># an RDD of Vectors |
| </span> |
| <span class="c1"># Compute column summary statistics. |
| </span><span class="n">summary</span> <span class="o">=</span> <span class="n">Statistics</span><span class="p">.</span><span class="n">colStats</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span> |
| <span class="k">print</span><span class="p">(</span><span class="n">summary</span><span class="p">.</span><span class="n">mean</span><span class="p">())</span> <span class="c1"># a dense vector containing the mean value for each column |
| </span><span class="k">print</span><span class="p">(</span><span class="n">summary</span><span class="p">.</span><span class="n">variance</span><span class="p">())</span> <span class="c1"># column-wise variance |
| </span><span class="k">print</span><span class="p">(</span><span class="n">summary</span><span class="p">.</span><span class="n">numNonzeros</span><span class="p">())</span> <span class="c1"># number of nonzeros in each column</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/summary_statistics_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| |
| <p><a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">colStats()</code></a> returns an instance of |
| <a href="api/scala/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code></a>, |
| which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the |
| total count.</p> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.</span><span class="o">{</span><span class="nc">MultivariateStatisticalSummary</span><span class="o">,</span> <span class="nc">Statistics</span><span class="o">}</span> |
| |
| <span class="k">val</span> <span class="nv">observations</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span> |
| <span class="nc">Seq</span><span class="o">(</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">10.0</span><span class="o">,</span> <span class="mf">100.0</span><span class="o">),</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">20.0</span><span class="o">,</span> <span class="mf">200.0</span><span class="o">),</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">3.0</span><span class="o">,</span> <span class="mf">30.0</span><span class="o">,</span> <span class="mf">300.0</span><span class="o">)</span> |
| <span class="o">)</span> |
| <span class="o">)</span> |
| |
| <span class="c1">// Compute column summary statistics.</span> |
| <span class="k">val</span> <span class="nv">summary</span><span class="k">:</span> <span class="kt">MultivariateStatisticalSummary</span> <span class="o">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">colStats</span><span class="o">(</span><span class="n">observations</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="nv">summary</span><span class="o">.</span><span class="py">mean</span><span class="o">)</span> <span class="c1">// a dense vector containing the mean value for each column</span> |
| <span class="nf">println</span><span class="o">(</span><span class="nv">summary</span><span class="o">.</span><span class="py">variance</span><span class="o">)</span> <span class="c1">// column-wise variance</span> |
| <span class="nf">println</span><span class="o">(</span><span class="nv">summary</span><span class="o">.</span><span class="py">numNonzeros</span><span class="o">)</span> <span class="c1">// number of nonzeros in each column</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p><a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">colStats()</code></a> returns an instance of |
| <a href="api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code></a>, |
| which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the |
| total count.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html"><code class="language-plaintext highlighter-rouge">MultivariateStatisticalSummary</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.MultivariateStatisticalSummary</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span><span class="o">;</span> |
| |
| <span class="nc">JavaRDD</span><span class="o"><</span><span class="nc">Vector</span><span class="o">></span> <span class="n">mat</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">10.0</span><span class="o">,</span> <span class="mf">100.0</span><span class="o">),</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">20.0</span><span class="o">,</span> <span class="mf">200.0</span><span class="o">),</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">3.0</span><span class="o">,</span> <span class="mf">30.0</span><span class="o">,</span> <span class="mf">300.0</span><span class="o">)</span> |
| <span class="o">)</span> |
| <span class="o">);</span> <span class="c1">// an RDD of Vectors</span> |
| |
| <span class="c1">// Compute column summary statistics.</span> |
| <span class="nc">MultivariateStatisticalSummary</span> <span class="n">summary</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">colStats</span><span class="o">(</span><span class="n">mat</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">summary</span><span class="o">.</span><span class="na">mean</span><span class="o">());</span> <span class="c1">// a dense vector containing the mean value for each column</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">summary</span><span class="o">.</span><span class="na">variance</span><span class="o">());</span> <span class="c1">// column-wise variance</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">summary</span><span class="o">.</span><span class="na">numNonzeros</span><span class="o">());</span> <span class="c1">// number of nonzeros in each column</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h2 id="correlations">Correlations</h2> |
| |
| <p>Calculating the correlation between two series of data is a common operation in Statistics. In <code class="language-plaintext highlighter-rouge">spark.mllib</code> |
| we provide the flexibility to calculate pairwise correlations among many series. The supported |
| correlation methods are currently Pearson’s and Spearman’s correlation.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| calculate correlations between series. Depending on the type of input, two <code class="language-plaintext highlighter-rouge">RDD[Double]</code>s or |
| an <code class="language-plaintext highlighter-rouge">RDD[Vector]</code>, the output will be a <code class="language-plaintext highlighter-rouge">Double</code> or the correlation <code class="language-plaintext highlighter-rouge">Matrix</code> respectively.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.mllib.stat</span> <span class="kn">import</span> <span class="n">Statistics</span> |
| |
| <span class="n">seriesX</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">])</span> <span class="c1"># a series |
| # seriesY must have the same number of partitions and cardinality as seriesX |
| </span><span class="n">seriesY</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">([</span><span class="mf">11.0</span><span class="p">,</span> <span class="mf">22.0</span><span class="p">,</span> <span class="mf">33.0</span><span class="p">,</span> <span class="mf">33.0</span><span class="p">,</span> <span class="mf">555.0</span><span class="p">])</span> |
| |
| <span class="c1"># 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. |
| </span><span class="k">print</span><span class="p">(</span><span class="s">"Correlation is: "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">Statistics</span><span class="p">.</span><span class="n">corr</span><span class="p">(</span><span class="n">seriesX</span><span class="p">,</span> <span class="n">seriesY</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s">"pearson"</span><span class="p">)))</span> |
| |
| <span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">(</span> |
| <span class="p">[</span><span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="mf">100.0</span><span class="p">]),</span> <span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">20.0</span><span class="p">,</span> <span class="mf">200.0</span><span class="p">]),</span> <span class="n">np</span><span class="p">.</span><span class="n">array</span><span class="p">([</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">33.0</span><span class="p">,</span> <span class="mf">366.0</span><span class="p">])]</span> |
| <span class="p">)</span> <span class="c1"># an RDD of Vectors |
| </span> |
| <span class="c1"># 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. |
| </span><span class="k">print</span><span class="p">(</span><span class="n">Statistics</span><span class="p">.</span><span class="n">corr</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s">"pearson"</span><span class="p">))</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/correlations_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| calculate correlations between series. Depending on the type of input, two <code class="language-plaintext highlighter-rouge">RDD[Double]</code>s or |
| an <code class="language-plaintext highlighter-rouge">RDD[Vector]</code>, the output will be a <code class="language-plaintext highlighter-rouge">Double</code> or the correlation <code class="language-plaintext highlighter-rouge">Matrix</code> respectively.</p> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg._</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span> |
| |
| <span class="k">val</span> <span class="nv">seriesX</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">3</span><span class="o">,</span> <span class="mi">3</span><span class="o">,</span> <span class="mi">5</span><span class="o">))</span> <span class="c1">// a series</span> |
| <span class="c1">// must have the same number of partitions and cardinality as seriesX</span> |
| <span class="k">val</span> <span class="nv">seriesY</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">11</span><span class="o">,</span> <span class="mi">22</span><span class="o">,</span> <span class="mi">33</span><span class="o">,</span> <span class="mi">33</span><span class="o">,</span> <span class="mi">555</span><span class="o">))</span> |
| |
| <span class="c1">// compute the correlation using Pearson's method. Enter "spearman" for Spearman's method. If a</span> |
| <span class="c1">// method is not specified, Pearson's method will be used by default.</span> |
| <span class="k">val</span> <span class="nv">correlation</span><span class="k">:</span> <span class="kt">Double</span> <span class="o">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">corr</span><span class="o">(</span><span class="n">seriesX</span><span class="o">,</span> <span class="n">seriesY</span><span class="o">,</span> <span class="s">"pearson"</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"Correlation is: $correlation"</span><span class="o">)</span> |
| |
| <span class="k">val</span> <span class="nv">data</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Vector</span><span class="o">]</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span> |
| <span class="nc">Seq</span><span class="o">(</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">10.0</span><span class="o">,</span> <span class="mf">100.0</span><span class="o">),</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">20.0</span><span class="o">,</span> <span class="mf">200.0</span><span class="o">),</span> |
| <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">5.0</span><span class="o">,</span> <span class="mf">33.0</span><span class="o">,</span> <span class="mf">366.0</span><span class="o">))</span> |
| <span class="o">)</span> <span class="c1">// note that each Vector is a row and not a column</span> |
| |
| <span class="c1">// calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method</span> |
| <span class="c1">// If a method is not specified, Pearson's method will be used by default.</span> |
| <span class="k">val</span> <span class="nv">correlMatrix</span><span class="k">:</span> <span class="kt">Matrix</span> <span class="o">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">corr</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="s">"pearson"</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="nv">correlMatrix</span><span class="o">.</span><span class="py">toString</span><span class="o">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/CorrelationsExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| calculate correlations between series. Depending on the type of input, two <code class="language-plaintext highlighter-rouge">JavaDoubleRDD</code>s or |
| a <code class="language-plaintext highlighter-rouge">JavaRDD<Vector></code>, the output will be a <code class="language-plaintext highlighter-rouge">Double</code> or the correlation <code class="language-plaintext highlighter-rouge">Matrix</code> respectively.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaDoubleRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span><span class="o">;</span> |
| |
| <span class="nc">JavaDoubleRDD</span> <span class="n">seriesX</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelizeDoubles</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">));</span> <span class="c1">// a series</span> |
| |
| <span class="c1">// must have the same number of partitions and cardinality as seriesX</span> |
| <span class="nc">JavaDoubleRDD</span> <span class="n">seriesY</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelizeDoubles</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mf">11.0</span><span class="o">,</span> <span class="mf">22.0</span><span class="o">,</span> <span class="mf">33.0</span><span class="o">,</span> <span class="mf">33.0</span><span class="o">,</span> <span class="mf">555.0</span><span class="o">));</span> |
| |
| <span class="c1">// compute the correlation using Pearson's method. Enter "spearman" for Spearman's method.</span> |
| <span class="c1">// If a method is not specified, Pearson's method will be used by default.</span> |
| <span class="kt">double</span> <span class="n">correlation</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">corr</span><span class="o">(</span><span class="n">seriesX</span><span class="o">.</span><span class="na">srdd</span><span class="o">(),</span> <span class="n">seriesY</span><span class="o">.</span><span class="na">srdd</span><span class="o">(),</span> <span class="s">"pearson"</span><span class="o">);</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">"Correlation is: "</span> <span class="o">+</span> <span class="n">correlation</span><span class="o">);</span> |
| |
| <span class="c1">// note that each Vector is a row and not a column</span> |
| <span class="nc">JavaRDD</span><span class="o"><</span><span class="nc">Vector</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">10.0</span><span class="o">,</span> <span class="mf">100.0</span><span class="o">),</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">20.0</span><span class="o">,</span> <span class="mf">200.0</span><span class="o">),</span> |
| <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">5.0</span><span class="o">,</span> <span class="mf">33.0</span><span class="o">,</span> <span class="mf">366.0</span><span class="o">)</span> |
| <span class="o">)</span> |
| <span class="o">);</span> |
| |
| <span class="c1">// calculate the correlation matrix using Pearson's method.</span> |
| <span class="c1">// Use "spearman" for Spearman's method.</span> |
| <span class="c1">// If a method is not specified, Pearson's method will be used by default.</span> |
| <span class="nc">Matrix</span> <span class="n">correlMatrix</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">corr</span><span class="o">(</span><span class="n">data</span><span class="o">.</span><span class="na">rdd</span><span class="o">(),</span> <span class="s">"pearson"</span><span class="o">);</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">correlMatrix</span><span class="o">.</span><span class="na">toString</span><span class="o">());</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h2 id="stratified-sampling">Stratified sampling</h2> |
| |
| <p>Unlike the other statistics functions, which reside in <code class="language-plaintext highlighter-rouge">spark.mllib</code>, stratified sampling methods, |
| <code class="language-plaintext highlighter-rouge">sampleByKey</code> and <code class="language-plaintext highlighter-rouge">sampleByKeyExact</code>, can be performed on RDD’s of key-value pairs. For stratified |
| sampling, the keys can be thought of as a label and the value as a specific attribute. For example |
| the key can be man or woman, or document ids, and the respective values can be the list of ages |
| of the people in the population or the list of words in the documents. The <code class="language-plaintext highlighter-rouge">sampleByKey</code> method |
| will flip a coin to decide whether an observation will be sampled or not, therefore requires one |
| pass over the data, and provides an <em>expected</em> sample size. <code class="language-plaintext highlighter-rouge">sampleByKeyExact</code> requires significant |
| more resources than the per-stratum simple random sampling used in <code class="language-plaintext highlighter-rouge">sampleByKey</code>, but will provide |
| the exact sampling size with 99.99% confidence. <code class="language-plaintext highlighter-rouge">sampleByKeyExact</code> is currently not supported in |
| python.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.RDD.sampleByKey.html#pyspark.RDD.sampleByKey"><code class="language-plaintext highlighter-rouge">sampleByKey()</code></a> allows users to |
| sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the |
| desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the |
| set of keys.</p> |
| |
| <p><em>Note:</em> <code class="language-plaintext highlighter-rouge">sampleByKeyExact()</code> is currently not supported in Python.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="c1"># an RDD of any key value pairs |
| </span><span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">([(</span><span class="mi">1</span><span class="p">,</span> <span class="s">'a'</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="s">'b'</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s">'c'</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s">'d'</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s">'e'</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s">'f'</span><span class="p">)])</span> |
| |
| <span class="c1"># specify the exact fraction desired from each key as a dictionary |
| </span><span class="n">fractions</span> <span class="o">=</span> <span class="p">{</span><span class="mi">1</span><span class="p">:</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mi">2</span><span class="p">:</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mi">3</span><span class="p">:</span> <span class="mf">0.3</span><span class="p">}</span> |
| |
| <span class="n">approxSample</span> <span class="o">=</span> <span class="n">data</span><span class="p">.</span><span class="n">sampleByKey</span><span class="p">(</span><span class="bp">False</span><span class="p">,</span> <span class="n">fractions</span><span class="p">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/stratified_sampling_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/rdd/PairRDDFunctions.html"><code class="language-plaintext highlighter-rouge">sampleByKeyExact()</code></a> 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 $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of |
| keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample |
| size, whereas sampling with replacement requires two additional passes.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="c1">// an RDD[(K, V)] of any key value pairs</span> |
| <span class="k">val</span> <span class="nv">data</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span> |
| <span class="nc">Seq</span><span class="o">((</span><span class="mi">1</span><span class="o">,</span> <span class="sc">'a'</span><span class="o">),</span> <span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="sc">'b'</span><span class="o">),</span> <span class="o">(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'c'</span><span class="o">),</span> <span class="o">(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'d'</span><span class="o">),</span> <span class="o">(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'e'</span><span class="o">),</span> <span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="sc">'f'</span><span class="o">)))</span> |
| |
| <span class="c1">// specify the exact fraction desired from each key</span> |
| <span class="k">val</span> <span class="nv">fractions</span> <span class="k">=</span> <span class="nc">Map</span><span class="o">(</span><span class="mi">1</span> <span class="o">-></span> <span class="mf">0.1</span><span class="o">,</span> <span class="mi">2</span> <span class="o">-></span> <span class="mf">0.6</span><span class="o">,</span> <span class="mi">3</span> <span class="o">-></span> <span class="mf">0.3</span><span class="o">)</span> |
| |
| <span class="c1">// Get an approximate sample from each stratum</span> |
| <span class="k">val</span> <span class="nv">approxSample</span> <span class="k">=</span> <span class="nv">data</span><span class="o">.</span><span class="py">sampleByKey</span><span class="o">(</span><span class="n">withReplacement</span> <span class="k">=</span> <span class="kc">false</span><span class="o">,</span> <span class="n">fractions</span> <span class="k">=</span> <span class="n">fractions</span><span class="o">)</span> |
| <span class="c1">// Get an exact sample from each stratum</span> |
| <span class="k">val</span> <span class="nv">exactSample</span> <span class="k">=</span> <span class="nv">data</span><span class="o">.</span><span class="py">sampleByKeyExact</span><span class="o">(</span><span class="n">withReplacement</span> <span class="k">=</span> <span class="kc">false</span><span class="o">,</span> <span class="n">fractions</span> <span class="k">=</span> <span class="n">fractions</span><span class="o">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/api/java/JavaPairRDD.html"><code class="language-plaintext highlighter-rouge">sampleByKeyExact()</code></a> 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 $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of |
| keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample |
| size, whereas sampling with replacement requires two additional passes.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.*</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">scala.Tuple2</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaPairRDD</span><span class="o">;</span> |
| |
| <span class="nc">List</span><span class="o"><</span><span class="nc">Tuple2</span><span class="o"><</span><span class="nc">Integer</span><span class="o">,</span> <span class="nc">Character</span><span class="o">>></span> <span class="n">list</span> <span class="o">=</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">1</span><span class="o">,</span> <span class="sc">'a'</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">1</span><span class="o">,</span> <span class="sc">'b'</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'c'</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'d'</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">2</span><span class="o">,</span> <span class="sc">'e'</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nc">Tuple2</span><span class="o"><>(</span><span class="mi">3</span><span class="o">,</span> <span class="sc">'f'</span><span class="o">)</span> |
| <span class="o">);</span> |
| |
| <span class="nc">JavaPairRDD</span><span class="o"><</span><span class="nc">Integer</span><span class="o">,</span> <span class="nc">Character</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelizePairs</span><span class="o">(</span><span class="n">list</span><span class="o">);</span> |
| |
| <span class="c1">// specify the exact fraction desired from each key Map<K, Double></span> |
| <span class="nc">ImmutableMap</span><span class="o"><</span><span class="nc">Integer</span><span class="o">,</span> <span class="nc">Double</span><span class="o">></span> <span class="n">fractions</span> <span class="o">=</span> <span class="nc">ImmutableMap</span><span class="o">.</span><span class="na">of</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mf">0.1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mf">0.6</span><span class="o">,</span> <span class="mi">3</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">);</span> |
| |
| <span class="c1">// Get an approximate sample from each stratum</span> |
| <span class="nc">JavaPairRDD</span><span class="o"><</span><span class="nc">Integer</span><span class="o">,</span> <span class="nc">Character</span><span class="o">></span> <span class="n">approxSample</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">sampleByKey</span><span class="o">(</span><span class="kc">false</span><span class="o">,</span> <span class="n">fractions</span><span class="o">);</span> |
| <span class="c1">// Get an exact sample from each stratum</span> |
| <span class="nc">JavaPairRDD</span><span class="o"><</span><span class="nc">Integer</span><span class="o">,</span> <span class="nc">Character</span><span class="o">></span> <span class="n">exactSample</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">sampleByKeyExact</span><span class="o">(</span><span class="kc">false</span><span class="o">,</span> <span class="n">fractions</span><span class="o">);</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h2 id="hypothesis-testing">Hypothesis testing</h2> |
| |
| <p>Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically |
| significant, whether this result occurred by chance or not. <code class="language-plaintext highlighter-rouge">spark.mllib</code> currently supports Pearson’s |
| chi-squared ( $\chi^2$) tests for goodness of fit and independence. The input data types determine |
| whether the goodness of fit or the independence test is conducted. The goodness of fit test requires |
| an input type of <code class="language-plaintext highlighter-rouge">Vector</code>, whereas the independence test requires a <code class="language-plaintext highlighter-rouge">Matrix</code> as input.</p> |
| |
| <p><code class="language-plaintext highlighter-rouge">spark.mllib</code> also supports the input type <code class="language-plaintext highlighter-rouge">RDD[LabeledPoint]</code> to enable feature selection via chi-squared |
| independence tests.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run Pearson’s chi-squared tests. The following example demonstrates how to run and interpret |
| hypothesis tests.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Matrices</span><span class="p">,</span> <span class="n">Vectors</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.stat</span> <span class="kn">import</span> <span class="n">Statistics</span> |
| |
| <span class="n">vec</span> <span class="o">=</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.15</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">)</span> <span class="c1"># a vector composed of the frequencies of events |
| </span> |
| <span class="c1"># compute the goodness of fit. If a second vector to test against |
| # is not supplied as a parameter, the test runs against a uniform distribution. |
| </span><span class="n">goodnessOfFitTestResult</span> <span class="o">=</span> <span class="n">Statistics</span><span class="p">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">vec</span><span class="p">)</span> |
| |
| <span class="c1"># summary of the test including the p-value, degrees of freedom, |
| # test statistic, the method used, and the null hypothesis. |
| </span><span class="k">print</span><span class="p">(</span><span class="s">"%s</span><span class="se">\n</span><span class="s">"</span> <span class="o">%</span> <span class="n">goodnessOfFitTestResult</span><span class="p">)</span> |
| |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">Matrices</span><span class="p">.</span><span class="n">dense</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">])</span> <span class="c1"># a contingency matrix |
| </span> |
| <span class="c1"># conduct Pearson's independence test on the input contingency matrix |
| </span><span class="n">independenceTestResult</span> <span class="o">=</span> <span class="n">Statistics</span><span class="p">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span> |
| |
| <span class="c1"># summary of the test including the p-value, degrees of freedom, |
| # test statistic, the method used, and the null hypothesis. |
| </span><span class="k">print</span><span class="p">(</span><span class="s">"%s</span><span class="se">\n</span><span class="s">"</span> <span class="o">%</span> <span class="n">independenceTestResult</span><span class="p">)</span> |
| |
| <span class="n">obs</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">(</span> |
| <span class="p">[</span><span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]),</span> |
| <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]),</span> |
| <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">])]</span> |
| <span class="p">)</span> <span class="c1"># LabeledPoint(label, feature) |
| </span> |
| <span class="c1"># The contingency table is constructed from an RDD of LabeledPoint and used to conduct |
| # the independence test. Returns an array containing the ChiSquaredTestResult for every feature |
| # against the label. |
| </span><span class="n">featureTestResults</span> <span class="o">=</span> <span class="n">Statistics</span><span class="p">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">obs</span><span class="p">)</span> |
| |
| <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">result</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">featureTestResults</span><span class="p">):</span> |
| <span class="k">print</span><span class="p">(</span><span class="s">"Column %d:</span><span class="se">\n</span><span class="s">%s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">result</span><span class="p">))</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/hypothesis_testing_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run Pearson’s chi-squared tests. The following example demonstrates how to run and interpret |
| hypothesis tests.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg._</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.test.ChiSqTestResult</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span> |
| |
| <span class="c1">// a vector composed of the frequencies of events</span> |
| <span class="k">val</span> <span class="nv">vec</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">0.1</span><span class="o">,</span> <span class="mf">0.15</span><span class="o">,</span> <span class="mf">0.2</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.25</span><span class="o">)</span> |
| |
| <span class="c1">// compute the goodness of fit. If a second vector to test against is not supplied</span> |
| <span class="c1">// as a parameter, the test runs against a uniform distribution.</span> |
| <span class="k">val</span> <span class="nv">goodnessOfFitTestResult</span> <span class="k">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">chiSqTest</span><span class="o">(</span><span class="n">vec</span><span class="o">)</span> |
| <span class="c1">// summary of the test including the p-value, degrees of freedom, test statistic, the method</span> |
| <span class="c1">// used, and the null hypothesis.</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"$goodnessOfFitTestResult\n"</span><span class="o">)</span> |
| |
| <span class="c1">// a contingency matrix. Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span> |
| <span class="k">val</span> <span class="nv">mat</span><span class="k">:</span> <span class="kt">Matrix</span> <span class="o">=</span> <span class="nv">Matrices</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">))</span> |
| |
| <span class="c1">// conduct Pearson's independence test on the input contingency matrix</span> |
| <span class="k">val</span> <span class="nv">independenceTestResult</span> <span class="k">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">chiSqTest</span><span class="o">(</span><span class="n">mat</span><span class="o">)</span> |
| <span class="c1">// summary of the test including the p-value, degrees of freedom</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"$independenceTestResult\n"</span><span class="o">)</span> |
| |
| <span class="k">val</span> <span class="nv">obs</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">LabeledPoint</span><span class="o">]</span> <span class="k">=</span> |
| <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span> |
| <span class="nc">Seq</span><span class="o">(</span> |
| <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)),</span> |
| <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">)),</span> |
| <span class="nc">LabeledPoint</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="o">)</span> |
| <span class="o">)</span> |
| <span class="o">)</span> |
| <span class="o">)</span> <span class="c1">// (label, feature) pairs.</span> |
| |
| <span class="c1">// The contingency table is constructed from the raw (label, feature) pairs and used to conduct</span> |
| <span class="c1">// the independence test. Returns an array containing the ChiSquaredTestResult for every feature</span> |
| <span class="c1">// against the label.</span> |
| <span class="k">val</span> <span class="nv">featureTestResults</span><span class="k">:</span> <span class="kt">Array</span><span class="o">[</span><span class="kt">ChiSqTestResult</span><span class="o">]</span> <span class="k">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">chiSqTest</span><span class="o">(</span><span class="n">obs</span><span class="o">)</span> |
| <span class="nv">featureTestResults</span><span class="o">.</span><span class="py">zipWithIndex</span><span class="o">.</span><span class="py">foreach</span> <span class="o">{</span> <span class="nf">case</span> <span class="o">(</span><span class="n">k</span><span class="o">,</span> <span class="n">v</span><span class="o">)</span> <span class="k">=></span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"Column ${(v + 1)} :"</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">k</span><span class="o">)</span> |
| <span class="o">}</span> <span class="c1">// summary of the test</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run Pearson’s chi-squared tests. The following example demonstrates how to run and interpret |
| hypothesis tests.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/stat/test/ChiSqTestResult.html"><code class="language-plaintext highlighter-rouge">ChiSqTestResult</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrices</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.test.ChiSqTestResult</span><span class="o">;</span> |
| |
| <span class="c1">// a vector composed of the frequencies of events</span> |
| <span class="nc">Vector</span> <span class="n">vec</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.1</span><span class="o">,</span> <span class="mf">0.15</span><span class="o">,</span> <span class="mf">0.2</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.25</span><span class="o">);</span> |
| |
| <span class="c1">// compute the goodness of fit. If a second vector to test against is not supplied</span> |
| <span class="c1">// as a parameter, the test runs against a uniform distribution.</span> |
| <span class="nc">ChiSqTestResult</span> <span class="n">goodnessOfFitTestResult</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">chiSqTest</span><span class="o">(</span><span class="n">vec</span><span class="o">);</span> |
| <span class="c1">// summary of the test including the p-value, degrees of freedom, test statistic,</span> |
| <span class="c1">// the method used, and the null hypothesis.</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">goodnessOfFitTestResult</span> <span class="o">+</span> <span class="s">"\n"</span><span class="o">);</span> |
| |
| <span class="c1">// Create a contingency matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span> |
| <span class="nc">Matrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="nc">Matrices</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">});</span> |
| |
| <span class="c1">// conduct Pearson's independence test on the input contingency matrix</span> |
| <span class="nc">ChiSqTestResult</span> <span class="n">independenceTestResult</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">chiSqTest</span><span class="o">(</span><span class="n">mat</span><span class="o">);</span> |
| <span class="c1">// summary of the test including the p-value, degrees of freedom...</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">independenceTestResult</span> <span class="o">+</span> <span class="s">"\n"</span><span class="o">);</span> |
| |
| <span class="c1">// an RDD of labeled points</span> |
| <span class="nc">JavaRDD</span><span class="o"><</span><span class="nc">LabeledPoint</span><span class="o">></span> <span class="n">obs</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)),</span> |
| <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">)),</span> |
| <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="o">))</span> |
| <span class="o">)</span> |
| <span class="o">);</span> |
| |
| <span class="c1">// The contingency table is constructed from the raw (label, feature) pairs and used to conduct</span> |
| <span class="c1">// the independence test. Returns an array containing the ChiSquaredTestResult for every feature</span> |
| <span class="c1">// against the label.</span> |
| <span class="nc">ChiSqTestResult</span><span class="o">[]</span> <span class="n">featureTestResults</span> <span class="o">=</span> <span class="nc">Statistics</span><span class="o">.</span><span class="na">chiSqTest</span><span class="o">(</span><span class="n">obs</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| <span class="kt">int</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span><span class="o">;</span> |
| <span class="k">for</span> <span class="o">(</span><span class="nc">ChiSqTestResult</span> <span class="n">result</span> <span class="o">:</span> <span class="n">featureTestResults</span><span class="o">)</span> <span class="o">{</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">"Column "</span> <span class="o">+</span> <span class="n">i</span> <span class="o">+</span> <span class="s">":"</span><span class="o">);</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">result</span> <span class="o">+</span> <span class="s">"\n"</span><span class="o">);</span> <span class="c1">// summary of the test</span> |
| <span class="n">i</span><span class="o">++;</span> |
| <span class="o">}</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <p>Additionally, <code class="language-plaintext highlighter-rouge">spark.mllib</code> provides a 1-sample, 2-sided implementation of the Kolmogorov-Smirnov (KS) test |
| for equality of probability distributions. By providing the name of a theoretical distribution |
| (currently solely supported for the normal distribution) and its parameters, or a function to |
| calculate the cumulative distribution according to a given theoretical distribution, the user can |
| test the null hypothesis that their sample is drawn from that distribution. In the case that the |
| user tests against the normal distribution (<code class="language-plaintext highlighter-rouge">distName="norm"</code>), but does not provide distribution |
| parameters, the test initializes to the standard normal distribution and logs an appropriate |
| message.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run |
| and interpret the hypothesis tests.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.stat.Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.mllib.stat</span> <span class="kn">import</span> <span class="n">Statistics</span> |
| |
| <span class="n">parallelData</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.15</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">])</span> |
| |
| <span class="c1"># run a KS test for the sample versus a standard normal distribution |
| </span><span class="n">testResult</span> <span class="o">=</span> <span class="n">Statistics</span><span class="p">.</span><span class="n">kolmogorovSmirnovTest</span><span class="p">(</span><span class="n">parallelData</span><span class="p">,</span> <span class="s">"norm"</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> |
| <span class="c1"># summary of the test including the p-value, test statistic, and null hypothesis |
| # if our p-value indicates significance, we can reject the null hypothesis |
| # Note that the Scala functionality of calling Statistics.kolmogorovSmirnovTest with |
| # a lambda to calculate the CDF is not made available in the Python API |
| </span><span class="k">print</span><span class="p">(</span><span class="n">testResult</span><span class="p">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run |
| and interpret the hypothesis tests.</p> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/mllib/stat/Statistics$.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span> |
| |
| <span class="k">val</span> <span class="nv">data</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span><span class="mf">0.1</span><span class="o">,</span> <span class="mf">0.15</span><span class="o">,</span> <span class="mf">0.2</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.25</span><span class="o">))</span> <span class="c1">// an RDD of sample data</span> |
| |
| <span class="c1">// run a KS test for the sample versus a standard normal distribution</span> |
| <span class="k">val</span> <span class="nv">testResult</span> <span class="k">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">kolmogorovSmirnovTest</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="s">"norm"</span><span class="o">,</span> <span class="mi">0</span><span class="o">,</span> <span class="mi">1</span><span class="o">)</span> |
| <span class="c1">// summary of the test including the p-value, test statistic, and null hypothesis if our p-value</span> |
| <span class="c1">// indicates significance, we can reject the null hypothesis.</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">testResult</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">()</span> |
| |
| <span class="c1">// perform a KS test using a cumulative distribution function of our making</span> |
| <span class="k">val</span> <span class="nv">myCDF</span> <span class="k">=</span> <span class="nc">Map</span><span class="o">(</span><span class="mf">0.1</span> <span class="o">-></span> <span class="mf">0.2</span><span class="o">,</span> <span class="mf">0.15</span> <span class="o">-></span> <span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.2</span> <span class="o">-></span> <span class="mf">0.05</span><span class="o">,</span> <span class="mf">0.3</span> <span class="o">-></span> <span class="mf">0.05</span><span class="o">,</span> <span class="mf">0.25</span> <span class="o">-></span> <span class="mf">0.1</span><span class="o">)</span> |
| <span class="k">val</span> <span class="nv">testResult2</span> <span class="k">=</span> <span class="nv">Statistics</span><span class="o">.</span><span class="py">kolmogorovSmirnovTest</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="n">myCDF</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">testResult2</span><span class="o">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code></a> provides methods to |
| run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run |
| and interpret the hypothesis tests.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/stat/Statistics.html"><code class="language-plaintext highlighter-rouge">Statistics</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaDoubleRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.Statistics</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult</span><span class="o">;</span> |
| |
| <span class="nc">JavaDoubleRDD</span> <span class="n">data</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelizeDoubles</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mf">0.1</span><span class="o">,</span> <span class="mf">0.15</span><span class="o">,</span> <span class="mf">0.2</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.25</span><span class="o">));</span> |
| <span class="nc">KolmogorovSmirnovTestResult</span> <span class="n">testResult</span> <span class="o">=</span> |
| <span class="nc">Statistics</span><span class="o">.</span><span class="na">kolmogorovSmirnovTest</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="s">"norm"</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">);</span> |
| <span class="c1">// summary of the test including the p-value, test statistic, and null hypothesis</span> |
| <span class="c1">// if our p-value indicates significance, we can reject the null hypothesis</span> |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">testResult</span><span class="o">);</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h3 id="streaming-significance-testing">Streaming Significance Testing</h3> |
| <p><code class="language-plaintext highlighter-rouge">spark.mllib</code> provides online implementations of some tests to support use cases |
| like A/B testing. These tests may be performed on a Spark Streaming |
| <code class="language-plaintext highlighter-rouge">DStream[(Boolean, Double)]</code> where the first element of each tuple |
| indicates control group (<code class="language-plaintext highlighter-rouge">false</code>) or treatment group (<code class="language-plaintext highlighter-rouge">true</code>) and the |
| second element is the value of an observation.</p> |
| |
| <p>Streaming significance testing supports the following parameters:</p> |
| |
| <ul> |
| <li><code class="language-plaintext highlighter-rouge">peacePeriod</code> - The number of initial data points from the stream to |
| ignore, used to mitigate novelty effects.</li> |
| <li><code class="language-plaintext highlighter-rouge">windowSize</code> - The number of past batches to perform hypothesis |
| testing over. Setting to <code class="language-plaintext highlighter-rouge">0</code> will perform cumulative processing using |
| all prior batches.</li> |
| </ul> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/stat/test/StreamingTest.html"><code class="language-plaintext highlighter-rouge">StreamingTest</code></a> |
| provides streaming hypothesis testing.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">val</span> <span class="nv">data</span> <span class="k">=</span> <span class="nv">ssc</span><span class="o">.</span><span class="py">textFileStream</span><span class="o">(</span><span class="n">dataDir</span><span class="o">).</span><span class="py">map</span><span class="o">(</span><span class="n">line</span> <span class="k">=></span> <span class="nv">line</span><span class="o">.</span><span class="py">split</span><span class="o">(</span><span class="s">","</span><span class="o">)</span> <span class="k">match</span> <span class="o">{</span> |
| <span class="k">case</span> <span class="nc">Array</span><span class="o">(</span><span class="n">label</span><span class="o">,</span> <span class="n">value</span><span class="o">)</span> <span class="k">=></span> <span class="nc">BinarySample</span><span class="o">(</span><span class="nv">label</span><span class="o">.</span><span class="py">toBoolean</span><span class="o">,</span> <span class="nv">value</span><span class="o">.</span><span class="py">toDouble</span><span class="o">)</span> |
| <span class="o">})</span> |
| |
| <span class="k">val</span> <span class="nv">streamingTest</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">StreamingTest</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setPeacePeriod</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setWindowSize</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setTestMethod</span><span class="o">(</span><span class="s">"welch"</span><span class="o">)</span> |
| |
| <span class="k">val</span> <span class="nv">out</span> <span class="k">=</span> <span class="nv">streamingTest</span><span class="o">.</span><span class="py">registerStream</span><span class="o">(</span><span class="n">data</span><span class="o">)</span> |
| <span class="nv">out</span><span class="o">.</span><span class="py">print</span><span class="o">()</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/StreamingTestExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/index.html#org.apache.spark.mllib.stat.test.StreamingTest"><code class="language-plaintext highlighter-rouge">StreamingTest</code></a> |
| provides streaming hypothesis testing.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.test.BinarySample</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.test.StreamingTest</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.test.StreamingTestResult</span><span class="o">;</span> |
| |
| <span class="nc">JavaDStream</span><span class="o"><</span><span class="nc">BinarySample</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">ssc</span><span class="o">.</span><span class="na">textFileStream</span><span class="o">(</span><span class="n">dataDir</span><span class="o">).</span><span class="na">map</span><span class="o">(</span><span class="n">line</span> <span class="o">-></span> <span class="o">{</span> |
| <span class="nc">String</span><span class="o">[]</span> <span class="n">ts</span> <span class="o">=</span> <span class="n">line</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">","</span><span class="o">);</span> |
| <span class="kt">boolean</span> <span class="n">label</span> <span class="o">=</span> <span class="nc">Boolean</span><span class="o">.</span><span class="na">parseBoolean</span><span class="o">(</span><span class="n">ts</span><span class="o">[</span><span class="mi">0</span><span class="o">]);</span> |
| <span class="kt">double</span> <span class="n">value</span> <span class="o">=</span> <span class="nc">Double</span><span class="o">.</span><span class="na">parseDouble</span><span class="o">(</span><span class="n">ts</span><span class="o">[</span><span class="mi">1</span><span class="o">]);</span> |
| <span class="k">return</span> <span class="k">new</span> <span class="nf">BinarySample</span><span class="o">(</span><span class="n">label</span><span class="o">,</span> <span class="n">value</span><span class="o">);</span> |
| <span class="o">});</span> |
| |
| <span class="nc">StreamingTest</span> <span class="n">streamingTest</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">StreamingTest</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">setPeacePeriod</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> |
| <span class="o">.</span><span class="na">setWindowSize</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> |
| <span class="o">.</span><span class="na">setTestMethod</span><span class="o">(</span><span class="s">"welch"</span><span class="o">);</span> |
| |
| <span class="nc">JavaDStream</span><span class="o"><</span><span class="nc">StreamingTestResult</span><span class="o">></span> <span class="n">out</span> <span class="o">=</span> <span class="n">streamingTest</span><span class="o">.</span><span class="na">registerStream</span><span class="o">(</span><span class="n">data</span><span class="o">);</span> |
| <span class="n">out</span><span class="o">.</span><span class="na">print</span><span class="o">();</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaStreamingTestExample.java" in the Spark repo.</small></div> |
| </div> |
| </div> |
| |
| <h2 id="random-data-generation">Random data generation</h2> |
| |
| <p>Random data generation is useful for randomized algorithms, prototyping, and performance testing. |
| <code class="language-plaintext highlighter-rouge">spark.mllib</code> supports generating random RDDs with i.i.d. values drawn from a given distribution: |
| uniform, standard normal, or Poisson.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.random.RandomRDDs.html"><code class="language-plaintext highlighter-rouge">RandomRDDs</code></a> provides factory |
| methods to generate random double RDDs or vector RDDs. |
| The following example generates a random double RDD, whose values follows the standard normal |
| distribution <code class="language-plaintext highlighter-rouge">N(0, 1)</code>, and then map it to <code class="language-plaintext highlighter-rouge">N(1, 4)</code>.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.random.RandomRDDs.html"><code class="language-plaintext highlighter-rouge">RandomRDDs</code> Python docs</a> for more details on the API.</p> |
| |
| <figure class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.random</span> <span class="kn">import</span> <span class="n">RandomRDDs</span> |
| |
| <span class="n">sc</span> <span class="o">=</span> <span class="p">...</span> <span class="c1"># SparkContext |
| </span> |
| <span class="c1"># Generate a random double RDD that contains 1 million i.i.d. values drawn from the |
| # standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions. |
| </span><span class="n">u</span> <span class="o">=</span> <span class="n">RandomRDDs</span><span class="p">.</span><span class="n">normalRDD</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="il">1000000L</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> |
| <span class="c1"># Apply a transform to get a random double RDD following `N(1, 4)`. |
| </span><span class="n">v</span> <span class="o">=</span> <span class="n">u</span><span class="p">.</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="mf">1.0</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span></code></pre></figure> |
| |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/random/RandomRDDs$.html"><code class="language-plaintext highlighter-rouge">RandomRDDs</code></a> provides factory |
| methods to generate random double RDDs or vector RDDs. |
| The following example generates a random double RDD, whose values follows the standard normal |
| distribution <code class="language-plaintext highlighter-rouge">N(0, 1)</code>, and then map it to <code class="language-plaintext highlighter-rouge">N(1, 4)</code>.</p> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/mllib/random/RandomRDDs$.html"><code class="language-plaintext highlighter-rouge">RandomRDDs</code> Scala docs</a> for details on the API.</p> |
| |
| <figure class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.SparkContext</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.random.RandomRDDs._</span> |
| |
| <span class="k">val</span> <span class="nv">sc</span><span class="k">:</span> <span class="kt">SparkContext</span> <span class="o">=</span> <span class="o">...</span> |
| |
| <span class="c1">// Generate a random double RDD that contains 1 million i.i.d. values drawn from the</span> |
| <span class="c1">// standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.</span> |
| <span class="k">val</span> <span class="nv">u</span> <span class="k">=</span> <span class="nf">normalRDD</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="mi">1000000L</span><span class="o">,</span> <span class="mi">10</span><span class="o">)</span> |
| <span class="c1">// Apply a transform to get a random double RDD following `N(1, 4)`.</span> |
| <span class="k">val</span> <span class="nv">v</span> <span class="k">=</span> <span class="nv">u</span><span class="o">.</span><span class="py">map</span><span class="o">(</span><span class="n">x</span> <span class="k">=></span> <span class="mf">1.0</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">x</span><span class="o">)</span></code></pre></figure> |
| |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/index.html#org.apache.spark.mllib.random.RandomRDDs"><code class="language-plaintext highlighter-rouge">RandomRDDs</code></a> provides factory |
| methods to generate random double RDDs or vector RDDs. |
| The following example generates a random double RDD, whose values follows the standard normal |
| distribution <code class="language-plaintext highlighter-rouge">N(0, 1)</code>, and then map it to <code class="language-plaintext highlighter-rouge">N(1, 4)</code>.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/random/RandomRDDs"><code class="language-plaintext highlighter-rouge">RandomRDDs</code> Java docs</a> for details on the API.</p> |
| |
| <figure class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.SparkContext</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.JavaDoubleRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">static</span> <span class="n">org</span><span class="o">.</span><span class="na">apache</span><span class="o">.</span><span class="na">spark</span><span class="o">.</span><span class="na">mllib</span><span class="o">.</span><span class="na">random</span><span class="o">.</span><span class="na">RandomRDDs</span><span class="o">.*;</span> |
| |
| <span class="nc">JavaSparkContext</span> <span class="n">jsc</span> <span class="o">=</span> <span class="o">...</span> |
| |
| <span class="c1">// Generate a random double RDD that contains 1 million i.i.d. values drawn from the</span> |
| <span class="c1">// standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.</span> |
| <span class="nc">JavaDoubleRDD</span> <span class="n">u</span> <span class="o">=</span> <span class="n">normalJavaRDD</span><span class="o">(</span><span class="n">jsc</span><span class="o">,</span> <span class="mi">1000000L</span><span class="o">,</span> <span class="mi">10</span><span class="o">);</span> |
| <span class="c1">// Apply a transform to get a random double RDD following `N(1, 4)`.</span> |
| <span class="nc">JavaDoubleRDD</span> <span class="n">v</span> <span class="o">=</span> <span class="n">u</span><span class="o">.</span><span class="na">mapToDouble</span><span class="o">(</span><span class="n">x</span> <span class="o">-></span> <span class="mf">1.0</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">x</span><span class="o">);</span></code></pre></figure> |
| |
| </div> |
| |
| </div> |
| |
| <h2 id="kernel-density-estimation">Kernel density estimation</h2> |
| |
| <p><a href="https://en.wikipedia.org/wiki/Kernel_density_estimation">Kernel density estimation</a> is a technique |
| useful for visualizing empirical probability distributions without requiring assumptions about the |
| particular distribution that the observed samples are drawn from. It computes an estimate of the |
| probability density function of a random variables, evaluated at a given set of points. It achieves |
| this estimate by expressing the PDF of the empirical distribution at a particular point as the |
| mean of PDFs of normal distributions centered around each of the samples.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/reference/api/pyspark.mllib.stat.KernelDensity.html"><code class="language-plaintext highlighter-rouge">KernelDensity</code></a> provides methods |
| to compute kernel density estimates from an RDD of samples. The following example demonstrates how |
| to do so.</p> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.stat.KernelDensity.html"><code class="language-plaintext highlighter-rouge">KernelDensity</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.mllib.stat</span> <span class="kn">import</span> <span class="n">KernelDensity</span> |
| |
| <span class="c1"># an RDD of sample data |
| </span><span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">parallelize</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">,</span> <span class="mf">9.0</span><span class="p">,</span> <span class="mf">9.0</span><span class="p">])</span> |
| |
| <span class="c1"># Construct the density estimator with the sample data and a standard deviation for the Gaussian |
| # kernels |
| </span><span class="n">kd</span> <span class="o">=</span> <span class="n">KernelDensity</span><span class="p">()</span> |
| <span class="n">kd</span><span class="p">.</span><span class="n">setSample</span><span class="p">(</span><span class="n">data</span><span class="p">)</span> |
| <span class="n">kd</span><span class="p">.</span><span class="n">setBandwidth</span><span class="p">(</span><span class="mf">3.0</span><span class="p">)</span> |
| |
| <span class="c1"># Find density estimates for the given values |
| </span><span class="n">densities</span> <span class="o">=</span> <span class="n">kd</span><span class="p">.</span><span class="n">estimate</span><span class="p">([</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">])</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/kernel_density_estimation_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| <p><a href="api/scala/org/apache/spark/mllib/stat/KernelDensity.html"><code class="language-plaintext highlighter-rouge">KernelDensity</code></a> provides methods |
| to compute kernel density estimates from an RDD of samples. The following example demonstrates how |
| to do so.</p> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/mllib/stat/KernelDensity.html"><code class="language-plaintext highlighter-rouge">KernelDensity</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.stat.KernelDensity</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span> |
| |
| <span class="c1">// an RDD of sample data</span> |
| <span class="k">val</span> <span class="nv">data</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">3</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">6</span><span class="o">,</span> <span class="mi">7</span><span class="o">,</span> <span class="mi">8</span><span class="o">,</span> <span class="mi">9</span><span class="o">,</span> <span class="mi">9</span><span class="o">))</span> |
| |
| <span class="c1">// Construct the density estimator with the sample data and a standard deviation</span> |
| <span class="c1">// for the Gaussian kernels</span> |
| <span class="k">val</span> <span class="nv">kd</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">KernelDensity</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setSample</span><span class="o">(</span><span class="n">data</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setBandwidth</span><span class="o">(</span><span class="mf">3.0</span><span class="o">)</span> |
| |
| <span class="c1">// Find density estimates for the given values</span> |
| <span class="k">val</span> <span class="nv">densities</span> <span class="k">=</span> <span class="nv">kd</span><span class="o">.</span><span class="py">estimate</span><span class="o">(</span><span class="nc">Array</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">))</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/index.html#org.apache.spark.mllib.stat.KernelDensity"><code class="language-plaintext highlighter-rouge">KernelDensity</code></a> provides methods |
| to compute kernel density estimates from an RDD of samples. The following example demonstrates how |
| to do so.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/stat/KernelDensity.html"><code class="language-plaintext highlighter-rouge">KernelDensity</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.stat.KernelDensity</span><span class="o">;</span> |
| |
| <span class="c1">// an RDD of sample data</span> |
| <span class="nc">JavaRDD</span><span class="o"><</span><span class="nc">Double</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">jsc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span> |
| <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">,</span> <span class="mf">7.0</span><span class="o">,</span> <span class="mf">8.0</span><span class="o">,</span> <span class="mf">9.0</span><span class="o">,</span> <span class="mf">9.0</span><span class="o">));</span> |
| |
| <span class="c1">// Construct the density estimator with the sample data</span> |
| <span class="c1">// and a standard deviation for the Gaussian kernels</span> |
| <span class="nc">KernelDensity</span> <span class="n">kd</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">KernelDensity</span><span class="o">().</span><span class="na">setSample</span><span class="o">(</span><span class="n">data</span><span class="o">).</span><span class="na">setBandwidth</span><span class="o">(</span><span class="mf">3.0</span><span class="o">);</span> |
| |
| <span class="c1">// Find density estimates for the given values</span> |
| <span class="kt">double</span><span class="o">[]</span> <span class="n">densities</span> <span class="o">=</span> <span class="n">kd</span><span class="o">.</span><span class="na">estimate</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">});</span> |
| |
| <span class="nc">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">toString</span><span class="o">(</span><span class="n">densities</span><span class="o">));</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java" in the Spark repo.</small></div> |
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