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| <section id="statistics"> |
| <h1>Statistics<a class="headerlink" href="#statistics" title="Permalink to this headline">#</a></h1> |
| <dl class="py class"> |
| <dt class="sig sig-object py" id="pyspark.mllib.stat.Statistics"> |
| <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pyspark.mllib.stat.</span></span><span class="sig-name descname"><span class="pre">Statistics</span></span><a class="reference internal" href="../../_modules/pyspark/mllib/stat/_statistics.html#Statistics"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyspark.mllib.stat.Statistics" title="Permalink to this definition">#</a></dt> |
| <dd><p class="rubric">Methods</p> |
| <table class="autosummary longtable table autosummary"> |
| <colgroup> |
| <col style="width: 10%" /> |
| <col style="width: 90%" /> |
| </colgroup> |
| <tbody> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.stat.Statistics.chiSqTest" title="pyspark.mllib.stat.Statistics.chiSqTest"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chiSqTest</span></code></a>(observed[, expected])</p></td> |
| <td><p>If <cite>observed</cite> is Vector, conduct Pearson's chi-squared goodness of fit test of the observed data against the expected distribution, or against the uniform distribution (by default), with each category having an expected frequency of <cite>1 / len(observed)</cite>.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.stat.Statistics.colStats" title="pyspark.mllib.stat.Statistics.colStats"><code class="xref py py-obj docutils literal notranslate"><span class="pre">colStats</span></code></a>(rdd)</p></td> |
| <td><p>Computes column-wise summary statistics for the input RDD[Vector].</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.stat.Statistics.corr" title="pyspark.mllib.stat.Statistics.corr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">corr</span></code></a>(x[, y, method])</p></td> |
| <td><p>Compute the correlation (matrix) for the input RDD(s) using the specified method.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.stat.Statistics.kolmogorovSmirnovTest" title="pyspark.mllib.stat.Statistics.kolmogorovSmirnovTest"><code class="xref py py-obj docutils literal notranslate"><span class="pre">kolmogorovSmirnovTest</span></code></a>(data[, distName])</p></td> |
| <td><p>Performs the Kolmogorov-Smirnov (KS) test for data sampled from a continuous distribution.</p></td> |
| </tr> |
| </tbody> |
| </table> |
| <p class="rubric">Methods Documentation</p> |
| <dl class="py method"> |
| <dt class="sig sig-object py" id="pyspark.mllib.stat.Statistics.chiSqTest"> |
| <em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">chiSqTest</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">observed</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">expected</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyspark/mllib/stat/_statistics.html#Statistics.chiSqTest"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyspark.mllib.stat.Statistics.chiSqTest" title="Permalink to this definition">#</a></dt> |
| <dd><p>If <cite>observed</cite> is Vector, conduct Pearson’s chi-squared goodness |
| of fit test of the observed data against the expected distribution, |
| or against the uniform distribution (by default), with each category |
| having an expected frequency of <cite>1 / len(observed)</cite>.</p> |
| <p>If <cite>observed</cite> is matrix, conduct Pearson’s independence test on the |
| input contingency matrix, which cannot contain negative entries or |
| columns or rows that sum up to 0.</p> |
| <p>If <cite>observed</cite> is an RDD of LabeledPoint, conduct Pearson’s independence |
| test for every feature against the label across the input RDD. |
| For each feature, the (feature, label) pairs are converted into a |
| contingency matrix for which the chi-squared statistic is computed. |
| All label and feature values must be categorical.</p> |
| <dl class="field-list"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><dl> |
| <dt><strong>observed</strong><span class="classifier"><a class="reference internal" href="pyspark.mllib.linalg.Vector.html#pyspark.mllib.linalg.Vector" title="pyspark.mllib.linalg.Vector"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.Vector</span></code></a> or <a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.Matrix</span></code></a></span></dt><dd><p>it could be a vector containing the observed categorical |
| counts/relative frequencies, or the contingency matrix |
| (containing either counts or relative frequencies), |
| or an RDD of LabeledPoint containing the labeled dataset |
| with categorical features. Real-valued features will be |
| treated as categorical for each distinct value.</p> |
| </dd> |
| <dt><strong>expected</strong><span class="classifier"><a class="reference internal" href="pyspark.mllib.linalg.Vector.html#pyspark.mllib.linalg.Vector" title="pyspark.mllib.linalg.Vector"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.Vector</span></code></a></span></dt><dd><p>Vector containing the expected categorical counts/relative |
| frequencies. <cite>expected</cite> is rescaled if the <cite>expected</cite> sum |
| differs from the <cite>observed</cite> sum.</p> |
| </dd> |
| </dl> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><dl class="simple"> |
| <dt><a class="reference internal" href="pyspark.mllib.stat.ChiSqTestResult.html#pyspark.mllib.stat.ChiSqTestResult" title="pyspark.mllib.stat.ChiSqTestResult"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.stat.ChiSqTestResult</span></code></a></dt><dd><p>object containing the test statistic, degrees |
| of freedom, p-value, the method used, and the null hypothesis.</p> |
| </dd> |
| </dl> |
| </dd> |
| </dl> |
| <p class="rubric">Notes</p> |
| <p><cite>observed</cite> cannot contain negative values</p> |
| <p class="rubric">Examples</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span><span class="p">,</span> <span class="n">Matrices</span> |
| <span class="gp">>>> </span><span class="n">observed</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> |
| <span class="gp">>>> </span><span class="n">pearson</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">observed</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pearson</span><span class="o">.</span><span class="n">statistic</span><span class="p">)</span> |
| <span class="go">0.4</span> |
| <span class="gp">>>> </span><span class="n">pearson</span><span class="o">.</span><span class="n">degreesOfFreedom</span> |
| <span class="go">2</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pearson</span><span class="o">.</span><span class="n">pValue</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span> |
| <span class="go">0.8187</span> |
| <span class="gp">>>> </span><span class="n">pearson</span><span class="o">.</span><span class="n">method</span> |
| <span class="go">'pearson'</span> |
| <span class="gp">>>> </span><span class="n">pearson</span><span class="o">.</span><span class="n">nullHypothesis</span> |
| <span class="go">'observed follows the same distribution as expected.'</span> |
| </pre></div> |
| </div> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">observed</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">21</span><span class="p">,</span> <span class="mi">38</span><span class="p">,</span> <span class="mi">43</span><span class="p">,</span> <span class="mi">80</span><span class="p">])</span> |
| <span class="gp">>>> </span><span class="n">expected</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">20</span><span class="p">])</span> |
| <span class="gp">>>> </span><span class="n">pearson</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">observed</span><span class="p">,</span> <span class="n">expected</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pearson</span><span class="o">.</span><span class="n">pValue</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span> |
| <span class="go">0.0027</span> |
| </pre></div> |
| </div> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mf">40.0</span><span class="p">,</span> <span class="mf">24.0</span><span class="p">,</span> <span class="mf">29.0</span><span class="p">,</span> <span class="mf">56.0</span><span class="p">,</span> <span class="mf">32.0</span><span class="p">,</span> <span class="mf">42.0</span><span class="p">,</span> <span class="mf">31.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">30.0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">,</span> <span class="mf">12.0</span><span class="p">]</span> |
| <span class="gp">>>> </span><span class="n">chi</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">data</span><span class="p">))</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">chi</span><span class="o">.</span><span class="n">statistic</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span> |
| <span class="go">21.9958</span> |
| </pre></div> |
| </div> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">])),</span> |
| <span class="gp">... </span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">20.0</span><span class="p">])),</span> |
| <span class="gp">... </span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">30.0</span><span class="p">])),</span> |
| <span class="gp">... </span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">3.5</span><span class="p">,</span> <span class="mf">30.0</span><span class="p">])),</span> |
| <span class="gp">... </span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">3.5</span><span class="p">,</span> <span class="mf">40.0</span><span class="p">])),</span> |
| <span class="gp">... </span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">3.5</span><span class="p">,</span> <span class="mf">40.0</span><span class="p">])),]</span> |
| <span class="gp">>>> </span><span class="n">rdd</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">chi</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">chiSqTest</span><span class="p">(</span><span class="n">rdd</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">chi</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">statistic</span><span class="p">)</span> |
| <span class="go">0.75</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">chi</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">statistic</span><span class="p">)</span> |
| <span class="go">1.5</span> |
| </pre></div> |
| </div> |
| </dd></dl> |
| |
| <dl class="py method"> |
| <dt class="sig sig-object py" id="pyspark.mllib.stat.Statistics.colStats"> |
| <em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">colStats</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rdd</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyspark/mllib/stat/_statistics.html#Statistics.colStats"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyspark.mllib.stat.Statistics.colStats" title="Permalink to this definition">#</a></dt> |
| <dd><p>Computes column-wise summary statistics for the input RDD[Vector].</p> |
| <dl class="field-list"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><dl> |
| <dt><strong>rdd</strong><span class="classifier"><a class="reference internal" href="pyspark.RDD.html#pyspark.RDD" title="pyspark.RDD"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.RDD</span></code></a></span></dt><dd><p>an RDD[Vector] for which column-wise summary statistics |
| are to be computed.</p> |
| </dd> |
| </dl> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><dl class="simple"> |
| <dt><a class="reference internal" href="pyspark.mllib.stat.MultivariateStatisticalSummary.html#pyspark.mllib.stat.MultivariateStatisticalSummary" title="pyspark.mllib.stat.MultivariateStatisticalSummary"><code class="xref py py-class docutils literal notranslate"><span class="pre">MultivariateStatisticalSummary</span></code></a></dt><dd><p>object containing column-wise summary statistics.</p> |
| </dd> |
| </dl> |
| </dd> |
| </dl> |
| <p class="rubric">Examples</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span> |
| <span class="gp">>>> </span><span class="n">rdd</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]),</span> |
| <span class="gp">... </span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span> |
| <span class="gp">... </span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">8</span><span class="p">])])</span> |
| <span class="gp">>>> </span><span class="n">cStats</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">colStats</span><span class="p">(</span><span class="n">rdd</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> |
| <span class="go">array([ 4., 4., 0., 3.])</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">variance</span><span class="p">()</span> |
| <span class="go">array([ 4., 13., 0., 25.])</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> |
| <span class="go">3</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">numNonzeros</span><span class="p">()</span> |
| <span class="go">array([ 3., 2., 0., 3.])</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> |
| <span class="go">array([ 6., 7., 0., 8.])</span> |
| <span class="gp">>>> </span><span class="n">cStats</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> |
| <span class="go">array([ 2., 0., 0., -2.])</span> |
| </pre></div> |
| </div> |
| </dd></dl> |
| |
| <dl class="py method"> |
| <dt class="sig sig-object py" id="pyspark.mllib.stat.Statistics.corr"> |
| <em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">corr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyspark/mllib/stat/_statistics.html#Statistics.corr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyspark.mllib.stat.Statistics.corr" title="Permalink to this definition">#</a></dt> |
| <dd><p>Compute the correlation (matrix) for the input RDD(s) using the |
| specified method. |
| Methods currently supported: <cite>pearson (default), spearman</cite>.</p> |
| <p>If a single RDD of Vectors is passed in, a correlation matrix |
| comparing the columns in the input RDD is returned. Use <cite>method</cite> |
| to specify the method to be used for single RDD inout. |
| If two RDDs of floats are passed in, a single float is returned.</p> |
| <dl class="field-list"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><dl> |
| <dt><strong>x</strong><span class="classifier"><a class="reference internal" href="pyspark.RDD.html#pyspark.RDD" title="pyspark.RDD"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.RDD</span></code></a></span></dt><dd><p>an RDD of vector for which the correlation matrix is to be computed, |
| or an RDD of float of the same cardinality as y when y is specified.</p> |
| </dd> |
| <dt><strong>y</strong><span class="classifier"><a class="reference internal" href="pyspark.RDD.html#pyspark.RDD" title="pyspark.RDD"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.RDD</span></code></a>, optional</span></dt><dd><p>an RDD of float of the same cardinality as x.</p> |
| </dd> |
| <dt><strong>method</strong><span class="classifier">str, optional</span></dt><dd><p>String specifying the method to use for computing correlation. |
| Supported: <cite>pearson</cite> (default), <cite>spearman</cite></p> |
| </dd> |
| </dl> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><dl class="simple"> |
| <dt><a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.Matrix</span></code></a></dt><dd><p>Correlation matrix comparing columns in x.</p> |
| </dd> |
| </dl> |
| </dd> |
| </dl> |
| <p class="rubric">Examples</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</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="o">-</span><span class="mf">2.0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</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">3.0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">zeros</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">abs</span><span class="p">(</span><span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="o">-</span> <span class="mf">0.6546537</span><span class="p">)</span> <span class="o"><</span> <span class="mf">1e-7</span> |
| <span class="go">True</span> |
| <span class="gp">>>> </span><span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="o">==</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"pearson"</span><span class="p">)</span> |
| <span class="go">True</span> |
| <span class="gp">>>> </span><span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"spearman"</span><span class="p">)</span> |
| <span class="go">0.5</span> |
| <span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">isnan</span> |
| <span class="gp">>>> </span><span class="n">isnan</span><span class="p">(</span><span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">zeros</span><span class="p">))</span> |
| <span class="go">True</span> |
| <span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span> |
| <span class="gp">>>> </span><span class="n">rdd</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]),</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span> |
| <span class="gp">... </span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">8</span><span class="p">]),</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">([</span><span class="mi">9</span><span class="p">,</span> <span class="mi">0</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="gp">>>> </span><span class="n">pearsonCorr</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">rdd</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pearsonCorr</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">,</span> <span class="s1">'NaN'</span><span class="p">))</span> |
| <span class="go">[[ 1. 0.05564149 NaN 0.40047142]</span> |
| <span class="go"> [ 0.05564149 1. NaN 0.91359586]</span> |
| <span class="go"> [ NaN NaN 1. NaN]</span> |
| <span class="go"> [ 0.40047142 0.91359586 NaN 1. ]]</span> |
| <span class="gp">>>> </span><span class="n">spearmanCorr</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">rdd</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s2">"spearman"</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">spearmanCorr</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">,</span> <span class="s1">'NaN'</span><span class="p">))</span> |
| <span class="go">[[ 1. 0.10540926 NaN 0.4 ]</span> |
| <span class="go"> [ 0.10540926 1. NaN 0.9486833 ]</span> |
| <span class="go"> [ NaN NaN 1. NaN]</span> |
| <span class="go"> [ 0.4 0.9486833 NaN 1. ]]</span> |
| <span class="gp">>>> </span><span class="k">try</span><span class="p">:</span> |
| <span class="gp">... </span> <span class="n">Statistics</span><span class="o">.</span><span class="n">corr</span><span class="p">(</span><span class="n">rdd</span><span class="p">,</span> <span class="s2">"spearman"</span><span class="p">)</span> |
| <span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s2">"Method name as second argument without 'method=' shouldn't be allowed."</span><span class="p">)</span> |
| <span class="gp">... </span><span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span> |
| <span class="gp">... </span> <span class="k">pass</span> |
| </pre></div> |
| </div> |
| </dd></dl> |
| |
| <dl class="py method"> |
| <dt class="sig sig-object py" id="pyspark.mllib.stat.Statistics.kolmogorovSmirnovTest"> |
| <em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">kolmogorovSmirnovTest</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">distName</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'norm'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">params</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyspark/mllib/stat/_statistics.html#Statistics.kolmogorovSmirnovTest"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyspark.mllib.stat.Statistics.kolmogorovSmirnovTest" title="Permalink to this definition">#</a></dt> |
| <dd><p>Performs the Kolmogorov-Smirnov (KS) test for data sampled from |
| a continuous distribution. It tests the null hypothesis that |
| the data is generated from a particular distribution.</p> |
| <p>The given data is sorted and the Empirical Cumulative |
| Distribution Function (ECDF) is calculated |
| which for a given point is the number of points having a CDF |
| value lesser than it divided by the total number of points.</p> |
| <p>Since the data is sorted, this is a step function |
| that rises by (1 / length of data) for every ordered point.</p> |
| <p>The KS statistic gives us the maximum distance between the |
| ECDF and the CDF. Intuitively if this statistic is large, the |
| probability that the null hypothesis is true becomes small. |
| For specific details of the implementation, please have a look |
| at the Scala documentation.</p> |
| <dl class="field-list"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><dl> |
| <dt><strong>data</strong><span class="classifier"><a class="reference internal" href="pyspark.RDD.html#pyspark.RDD" title="pyspark.RDD"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.RDD</span></code></a></span></dt><dd><p>RDD, samples from the data</p> |
| </dd> |
| <dt><strong>distName</strong><span class="classifier">str, optional</span></dt><dd><p>string, currently only “norm” is supported. |
| (Normal distribution) to calculate the |
| theoretical distribution of the data.</p> |
| </dd> |
| <dt><strong>params</strong></dt><dd><p>additional values which need to be provided for |
| a certain distribution. |
| If not provided, the default values are used.</p> |
| </dd> |
| </dl> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><dl class="simple"> |
| <dt><a class="reference internal" href="pyspark.mllib.stat.KolmogorovSmirnovTestResult.html#pyspark.mllib.stat.KolmogorovSmirnovTestResult" title="pyspark.mllib.stat.KolmogorovSmirnovTestResult"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.stat.KolmogorovSmirnovTestResult</span></code></a></dt><dd><p>object containing the test statistic, degrees of freedom, p-value, |
| the method used, and the null hypothesis.</p> |
| </dd> |
| </dl> |
| </dd> |
| </dl> |
| <p class="rubric">Examples</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">kstest</span> <span class="o">=</span> <span class="n">Statistics</span><span class="o">.</span><span class="n">kolmogorovSmirnovTest</span> |
| <span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</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="mf">1.0</span><span class="p">])</span> |
| <span class="gp">>>> </span><span class="n">ksmodel</span> <span class="o">=</span> <span class="n">kstest</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="s2">"norm"</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">ksmodel</span><span class="o">.</span><span class="n">pValue</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> |
| <span class="go">1.0</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">ksmodel</span><span class="o">.</span><span class="n">statistic</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> |
| <span class="go">0.175</span> |
| <span class="gp">>>> </span><span class="n">ksmodel</span><span class="o">.</span><span class="n">nullHypothesis</span> |
| <span class="go">'Sample follows theoretical distribution'</span> |
| </pre></div> |
| </div> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</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="gp">>>> </span><span class="n">ksmodel</span> <span class="o">=</span> <span class="n">kstest</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="s2">"norm"</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">ksmodel</span><span class="o">.</span><span class="n">pValue</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> |
| <span class="go">1.0</span> |
| <span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">ksmodel</span><span class="o">.</span><span class="n">statistic</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> |
| <span class="go">0.175</span> |
| </pre></div> |
| </div> |
| </dd></dl> |
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