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| <h1 class="title">Regression - spark.mllib</h1> |
| |
| |
| <h2 id="isotonic-regression">Isotonic regression</h2> |
| <p><a href="http://en.wikipedia.org/wiki/Isotonic_regression">Isotonic regression</a> |
| belongs to the family of regression algorithms. Formally isotonic regression is a problem where |
| given a finite set of real numbers <code>$Y = {y_1, y_2, ..., y_n}$</code> representing observed responses |
| and <code>$X = {x_1, x_2, ..., x_n}$</code> the unknown response values to be fitted |
| finding a function that minimises</p> |
| |
| <p><code>\begin{equation} |
| f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2 |
| \end{equation}</code></p> |
| |
| <p>with respect to complete order subject to |
| <code>$x_1\le x_2\le ...\le x_n$</code> where <code>$w_i$</code> are positive weights. |
| The resulting function is called isotonic regression and it is unique. |
| It can be viewed as least squares problem under order restriction. |
| Essentially isotonic regression is a |
| <a href="http://en.wikipedia.org/wiki/Monotonic_function">monotonic function</a> |
| best fitting the original data points.</p> |
| |
| <p><code>spark.mllib</code> supports a |
| <a href="http://doi.org/10.1198/TECH.2010.10111">pool adjacent violators algorithm</a> |
| which uses an approach to |
| <a href="http://doi.org/10.1007/978-3-642-99789-1_10">parallelizing isotonic regression</a>. |
| The training input is a RDD of tuples of three double values that represent |
| label, feature and weight in this order. Additionally IsotonicRegression algorithm has one |
| optional parameter called $isotonic$ defaulting to true. |
| This argument specifies if the isotonic regression is |
| isotonic (monotonically increasing) or antitonic (monotonically decreasing).</p> |
| |
| <p>Training returns an IsotonicRegressionModel that can be used to predict |
| labels for both known and unknown features. The result of isotonic regression |
| is treated as piecewise linear function. The rules for prediction therefore are:</p> |
| |
| <ul> |
| <li>If the prediction input exactly matches a training feature |
| then associated prediction is returned. In case there are multiple predictions with the same |
| feature then one of them is returned. Which one is undefined |
| (same as java.util.Arrays.binarySearch).</li> |
| <li>If the prediction input is lower or higher than all training features |
| then prediction with lowest or highest feature is returned respectively. |
| In case there are multiple predictions with the same feature |
| then the lowest or highest is returned respectively.</li> |
| <li>If the prediction input falls between two training features then prediction is treated |
| as piecewise linear function and interpolated value is calculated from the |
| predictions of the two closest features. In case there are multiple values |
| with the same feature then the same rules as in previous point are used.</li> |
| </ul> |
| |
| <h3 id="examples">Examples</h3> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| <p>Data are read from a file where each line has a format label,feature |
| i.e. 4710.28,500.00. The data are split to training and testing set. |
| Model is created using the training set and a mean squared error is calculated from the predicted |
| labels and real labels in the test set.</p> |
| |
| <p>Refer to the <a href="api/scala/index.html#org.apache.spark.mllib.regression.IsotonicRegression"><code>IsotonicRegression</code> Scala docs</a> and <a href="api/scala/index.html#org.apache.spark.mllib.regression.IsotonicRegressionModel"><code>IsotonicRegressionModel</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.</span><span class="o">{</span><span class="nc">IsotonicRegression</span><span class="o">,</span> <span class="nc">IsotonicRegressionModel</span><span class="o">}</span> |
| |
| <span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="o">(</span><span class="s">"data/mllib/sample_isotonic_regression_data.txt"</span><span class="o">)</span> |
| |
| <span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</span> |
| <span class="k">val</span> <span class="n">parsedData</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">line</span> <span class="k">=></span> |
| <span class="k">val</span> <span class="n">parts</span> <span class="k">=</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="sc">','</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="k">_</span><span class="o">.</span><span class="n">toDouble</span><span class="o">)</span> |
| <span class="o">(</span><span class="n">parts</span><span class="o">(</span><span class="mi">0</span><span class="o">),</span> <span class="n">parts</span><span class="o">(</span><span class="mi">1</span><span class="o">),</span> <span class="mf">1.0</span><span class="o">)</span> |
| <span class="o">}</span> |
| |
| <span class="c1">// Split data into training (60%) and test (40%) sets.</span> |
| <span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">11L</span><span class="o">)</span> |
| <span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> |
| <span class="k">val</span> <span class="n">test</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span> |
| |
| <span class="c1">// Create isotonic regression model from training data.</span> |
| <span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span> |
| <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IsotonicRegression</span><span class="o">().</span><span class="n">setIsotonic</span><span class="o">(</span><span class="kc">true</span><span class="o">).</span><span class="n">run</span><span class="o">(</span><span class="n">training</span><span class="o">)</span> |
| |
| <span class="c1">// Create tuples of predicted and real labels.</span> |
| <span class="k">val</span> <span class="n">predictionAndLabel</span> <span class="k">=</span> <span class="n">test</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=></span> |
| <span class="k">val</span> <span class="n">predictedLabel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">_2</span><span class="o">)</span> |
| <span class="o">(</span><span class="n">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="n">_1</span><span class="o">)</span> |
| <span class="o">}</span> |
| |
| <span class="c1">// Calculate mean squared error between predicted and real labels.</span> |
| <span class="k">val</span> <span class="n">meanSquaredError</span> <span class="k">=</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="k">case</span> <span class="o">(</span><span class="n">p</span><span class="o">,</span> <span class="n">l</span><span class="o">)</span> <span class="k">=></span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="o">((</span><span class="n">p</span> <span class="o">-</span> <span class="n">l</span><span class="o">),</span> <span class="mi">2</span><span class="o">)</span> <span class="o">}.</span><span class="n">mean</span><span class="o">()</span> |
| <span class="n">println</span><span class="o">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">)</span> |
| |
| <span class="c1">// Save and load model</span> |
| <span class="n">model</span><span class="o">.</span><span class="n">save</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="o">)</span> |
| <span class="k">val</span> <span class="n">sameModel</span> <span class="k">=</span> <span class="nc">IsotonicRegressionModel</span><span class="o">.</span><span class="n">load</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="o">)</span> |
| </pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/IsotonicRegressionExample.scala" in the Spark repo.</small></div> |
| </div> |
| <div data-lang="java"> |
| <p>Data are read from a file where each line has a format label,feature |
| i.e. 4710.28,500.00. The data are split to training and testing set. |
| Model is created using the training set and a mean squared error is calculated from the predicted |
| labels and real labels in the test set.</p> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/mllib/regression/IsotonicRegression.html"><code>IsotonicRegression</code> Java docs</a> and <a href="api/java/org/apache/spark/mllib/regression/IsotonicRegressionModel.html"><code>IsotonicRegressionModel</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre><span class="kn">import</span> <span class="nn">scala.Tuple2</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">scala.Tuple3</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.function.Function</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.function.PairFunction</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.JavaPairRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</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.regression.IsotonicRegression</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.IsotonicRegressionModel</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">String</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">textFile</span><span class="o">(</span><span class="s">"data/mllib/sample_isotonic_regression_data.txt"</span><span class="o">);</span> |
| |
| <span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</span> |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>></span> <span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> |
| <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">String</span><span class="o">,</span> <span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>>()</span> <span class="o">{</span> |
| <span class="kd">public</span> <span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="nf">call</span><span class="o">(</span><span class="n">String</span> <span class="n">line</span><span class="o">)</span> <span class="o">{</span> |
| <span class="n">String</span><span class="o">[]</span> <span class="n">parts</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="k">return</span> <span class="k">new</span> <span class="n">Tuple3</span><span class="o"><>(</span><span class="k">new</span> <span class="nf">Double</span><span class="o">(</span><span class="n">parts</span><span class="o">[</span><span class="mi">0</span><span class="o">]),</span> <span class="k">new</span> <span class="nf">Double</span><span class="o">(</span><span class="n">parts</span><span class="o">[</span><span class="mi">1</span><span class="o">]),</span> <span class="mf">1.0</span><span class="o">);</span> |
| <span class="o">}</span> |
| <span class="o">}</span> |
| <span class="o">);</span> |
| |
| <span class="c1">// Split data into training (60%) and test (40%) sets.</span> |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>>[]</span> <span class="n">splits</span> <span class="o">=</span> |
| <span class="n">parsedData</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">},</span> <span class="mi">11L</span><span class="o">);</span> |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>></span> <span class="n">training</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span> |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>></span> <span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span> |
| |
| <span class="c1">// Create isotonic regression model from training data.</span> |
| <span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span> |
| <span class="kd">final</span> <span class="n">IsotonicRegressionModel</span> <span class="n">model</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IsotonicRegression</span><span class="o">().</span><span class="na">setIsotonic</span><span class="o">(</span><span class="kc">true</span><span class="o">).</span><span class="na">run</span><span class="o">(</span><span class="n">training</span><span class="o">);</span> |
| |
| <span class="c1">// Create tuples of predicted and real labels.</span> |
| <span class="n">JavaPairRDD</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="n">predictionAndLabel</span> <span class="o">=</span> <span class="n">test</span><span class="o">.</span><span class="na">mapToPair</span><span class="o">(</span> |
| <span class="k">new</span> <span class="n">PairFunction</span><span class="o"><</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>()</span> <span class="o">{</span> |
| <span class="nd">@Override</span> |
| <span class="kd">public</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="nf">call</span><span class="o">(</span><span class="n">Tuple3</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="n">point</span><span class="o">)</span> <span class="o">{</span> |
| <span class="n">Double</span> <span class="n">predictedLabel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="na">_2</span><span class="o">());</span> |
| <span class="k">return</span> <span class="k">new</span> <span class="n">Tuple2</span><span class="o"><>(</span><span class="n">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="na">_1</span><span class="o">());</span> |
| <span class="o">}</span> |
| <span class="o">}</span> |
| <span class="o">);</span> |
| |
| <span class="c1">// Calculate mean squared error between predicted and real labels.</span> |
| <span class="n">Double</span> <span class="n">meanSquaredError</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">JavaDoubleRDD</span><span class="o">(</span><span class="n">predictionAndLabel</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> |
| <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>,</span> <span class="n">Object</span><span class="o">>()</span> <span class="o">{</span> |
| <span class="nd">@Override</span> |
| <span class="kd">public</span> <span class="n">Object</span> <span class="nf">call</span><span class="o">(</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="n">pl</span><span class="o">)</span> <span class="o">{</span> |
| <span class="k">return</span> <span class="n">Math</span><span class="o">.</span><span class="na">pow</span><span class="o">(</span><span class="n">pl</span><span class="o">.</span><span class="na">_1</span><span class="o">()</span> <span class="o">-</span> <span class="n">pl</span><span class="o">.</span><span class="na">_2</span><span class="o">(),</span> <span class="mi">2</span><span class="o">);</span> |
| <span class="o">}</span> |
| <span class="o">}</span> |
| <span class="o">).</span><span class="na">rdd</span><span class="o">()).</span><span class="na">mean</span><span class="o">();</span> |
| <span class="n">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">"Mean Squared Error = "</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">);</span> |
| |
| <span class="c1">// Save and load model</span> |
| <span class="n">model</span><span class="o">.</span><span class="na">save</span><span class="o">(</span><span class="n">jsc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="o">);</span> |
| <span class="n">IsotonicRegressionModel</span> <span class="n">sameModel</span> <span class="o">=</span> |
| <span class="n">IsotonicRegressionModel</span><span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="n">jsc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="o">);</span> |
| </pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaIsotonicRegressionExample.java" in the Spark repo.</small></div> |
| </div> |
| <div data-lang="python"> |
| <p>Data are read from a file where each line has a format label,feature |
| i.e. 4710.28,500.00. The data are split to training and testing set. |
| Model is created using the training set and a mean squared error is calculated from the predicted |
| labels and real labels in the test set.</p> |
| |
| <p>Refer to the <a href="api/python/pyspark.mllib.html#pyspark.mllib.regression.IsotonicRegression"><code>IsotonicRegression</code> Python docs</a> and <a href="api/python/pyspark.mllib.html#pyspark.mllib.regression.IsotonicRegressionModel"><code>IsotonicRegressionModel</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre><span class="kn">import</span> <span class="nn">math</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">IsotonicRegression</span><span class="p">,</span> <span class="n">IsotonicRegressionModel</span> |
| |
| <span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"data/mllib/sample_isotonic_regression_data.txt"</span><span class="p">)</span> |
| |
| <span class="c"># Create label, feature, weight tuples from input data with weight set to default value 1.0.</span> |
| <span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">','</span><span class="p">)])</span> <span class="o">+</span> <span class="p">(</span><span class="mf">1.0</span><span class="p">,))</span> |
| |
| <span class="c"># Split data into training (60%) and test (40%) sets.</span> |
| <span class="n">training</span><span class="p">,</span> <span class="n">test</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">],</span> <span class="mi">11</span><span class="p">)</span> |
| |
| <span class="c"># Create isotonic regression model from training data.</span> |
| <span class="c"># Isotonic parameter defaults to true so it is only shown for demonstration</span> |
| <span class="n">model</span> <span class="o">=</span> <span class="n">IsotonicRegression</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">training</span><span class="p">)</span> |
| |
| <span class="c"># Create tuples of predicted and real labels.</span> |
| <span class="n">predictionAndLabel</span> <span class="o">=</span> <span class="n">test</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span> |
| |
| <span class="c"># Calculate mean squared error between predicted and real labels.</span> |
| <span class="n">meanSquaredError</span> <span class="o">=</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">pl</span><span class="p">:</span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">((</span><span class="n">pl</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">pl</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> |
| <span class="k">print</span><span class="p">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">meanSquaredError</span><span class="p">))</span> |
| |
| <span class="c"># Save and load model</span> |
| <span class="n">model</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="p">)</span> |
| <span class="n">sameModel</span> <span class="o">=</span> <span class="n">IsotonicRegressionModel</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">"target/tmp/myIsotonicRegressionModel"</span><span class="p">)</span> |
| </pre></div> |
| <div><small>Find full example code at "examples/src/main/python/mllib/isotonic_regression_example.py" in the Spark repo.</small></div> |
| </div> |
| </div> |
| |
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