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<h1 class="title"><a href="mllib-guide.html">MLlib</a> - Naive Bayes</h1>
<p><a href="http://en.wikipedia.org/wiki/Naive_Bayes_classifier">Naive Bayes</a> is a simple
multiclass classification algorithm with the assumption of independence between
every pair of features. Naive Bayes can be trained very efficiently. Within a
single pass to the training data, it computes the conditional probability
distribution of each feature given label, and then it applies Bayes’ theorem to
compute the conditional probability distribution of label given an observation
and use it for prediction.</p>
<p>MLlib supports <a href="http://en.wikipedia.org/wiki/Naive_Bayes_classifier#Multinomial_naive_Bayes">multinomial naive
Bayes</a>,
which is typically used for <a href="http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html">document
classification</a>.
Within that context, each observation is a document and each
feature represents a term whose value is the frequency of the term.
Feature values must be nonnegative to represent term frequencies.
<a href="http://en.wikipedia.org/wiki/Lidstone_smoothing">Additive smoothing</a> can be used by
setting the parameter $\lambda$ (default to $1.0$). For document classification, the input feature
vectors are usually sparse, and sparse vectors should be supplied as input to take advantage of
sparsity. Since the training data is only used once, it is not necessary to cache it.</p>
<h2 id="examples">Examples</h2>
<div class="codetabs">
<div data-lang="scala">
<p><a href="api/scala/index.html#org.apache.spark.mllib.classification.NaiveBayes$">NaiveBayes</a> implements
multinomial naive Bayes. It takes an RDD of
<a href="api/scala/index.html#org.apache.spark.mllib.regression.LabeledPoint">LabeledPoint</a> and an optional
smoothing parameter <code>lambda</code> as input, and output a
<a href="api/scala/index.html#org.apache.spark.mllib.classification.NaiveBayesModel">NaiveBayesModel</a>, which
can be used for evaluation and prediction.</p>
<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.classification.</span><span class="o">{</span><span class="nc">NaiveBayes</span><span class="o">,</span> <span class="nc">NaiveBayesModel</span><span class="o">}</span>
<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.regression.LabeledPoint</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_naive_bayes_data.txt"</span><span class="o">)</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="nc">LabeledPoint</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">toDouble</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</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="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="c1">// Split data into training (60%) and test (40%).</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="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">NaiveBayes</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">training</span><span class="o">,</span> <span class="n">lambda</span> <span class="k">=</span> <span class="mf">1.0</span><span class="o">)</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">p</span> <span class="k">=></span> <span class="o">(</span><span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">p</span><span class="o">.</span><span class="n">features</span><span class="o">),</span> <span class="n">p</span><span class="o">.</span><span class="n">label</span><span class="o">))</span>
<span class="k">val</span> <span class="n">accuracy</span> <span class="k">=</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="n">filter</span><span class="o">(</span><span class="n">x</span> <span class="k">=></span> <span class="n">x</span><span class="o">.</span><span class="n">_1</span> <span class="o">==</span> <span class="n">x</span><span class="o">.</span><span class="n">_2</span><span class="o">).</span><span class="n">count</span><span class="o">()</span> <span class="o">/</span> <span class="n">test</span><span class="o">.</span><span class="n">count</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">"myModelPath"</span><span class="o">)</span>
<span class="k">val</span> <span class="n">sameModel</span> <span class="k">=</span> <span class="nc">NaiveBayesModel</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">"myModelPath"</span><span class="o">)</span></code></pre></div>
</div>
<div data-lang="java">
<p><a href="api/java/org/apache/spark/mllib/classification/NaiveBayes.html">NaiveBayes</a> implements
multinomial naive Bayes. It takes a Scala RDD of
<a href="api/java/org/apache/spark/mllib/regression/LabeledPoint.html">LabeledPoint</a> and an
optionally smoothing parameter <code>lambda</code> as input, and output a
<a href="api/java/org/apache/spark/mllib/classification/NaiveBayesModel.html">NaiveBayesModel</a>, which
can be used for evaluation and prediction.</p>
<div class="highlight"><pre><code class="language-java" data-lang="java"><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.JavaRDD</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.mllib.classification.NaiveBayes</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.classification.NaiveBayesModel</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">scala.Tuple2</span><span class="o">;</span>
<span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">training</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// training set</span>
<span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">test</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// test set</span>
<span class="kd">final</span> <span class="n">NaiveBayesModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">NaiveBayes</span><span class="o">.</span><span class="na">train</span><span class="o">(</span><span class="n">training</span><span class="o">.</span><span class="na">rdd</span><span class="o">(),</span> <span class="mf">1.0</span><span class="o">);</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">LabeledPoint</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">LabeledPoint</span> <span class="n">p</span><span class="o">)</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">Double</span><span class="o">,</span> <span class="n">Double</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">p</span><span class="o">.</span><span class="na">features</span><span class="o">()),</span> <span class="n">p</span><span class="o">.</span><span class="na">label</span><span class="o">());</span>
<span class="o">}</span>
<span class="o">});</span>
<span class="kt">double</span> <span class="n">accuracy</span> <span class="o">=</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="na">filter</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">Boolean</span><span class="o">>()</span> <span class="o">{</span>
<span class="nd">@Override</span> <span class="kd">public</span> <span class="n">Boolean</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">pl</span><span class="o">.</span><span class="na">_1</span><span class="o">().</span><span class="na">equals</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="o">}</span>
<span class="o">}).</span><span class="na">count</span><span class="o">()</span> <span class="o">/</span> <span class="o">(</span><span class="kt">double</span><span class="o">)</span> <span class="n">test</span><span class="o">.</span><span class="na">count</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">sc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">"myModelPath"</span><span class="o">);</span>
<span class="n">NaiveBayesModel</span> <span class="n">sameModel</span> <span class="o">=</span> <span class="n">NaiveBayesModel</span><span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="n">sc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">"myModelPath"</span><span class="o">);</span></code></pre></div>
</div>
<div data-lang="python">
<p><a href="api/python/pyspark.mllib.html#pyspark.mllib.classification.NaiveBayes">NaiveBayes</a> implements multinomial
naive Bayes. It takes an RDD of
<a href="api/python/pyspark.mllib.html#pyspark.mllib.regression.LabeledPoint">LabeledPoint</a> and an optionally
smoothing parameter <code>lambda</code> as input, and output a
<a href="api/python/pyspark.mllib.html#pyspark.mllib.classification.NaiveBayesModel">NaiveBayesModel</a>, which can be
used for evaluation and prediction.</p>
<p>Note that the Python API does not yet support model save/load but will in the future.</p>
<div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.classification</span> <span class="kn">import</span> <span class="n">NaiveBayes</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="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>
<span class="k">def</span> <span class="nf">parseLine</span><span class="p">(</span><span class="n">line</span><span class="p">):</span>
<span class="n">parts</span> <span class="o">=</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="n">label</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">parts</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">features</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="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">parts</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">features</span><span class="p">)</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_naive_bayes_data.txt'</span><span class="p">)</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="n">parseLine</span><span class="p">)</span>
<span class="c"># Split data aproximately into training (60%) and test (40%)</span>
<span class="n">training</span><span class="p">,</span> <span class="n">test</span> <span class="o">=</span> <span class="n">data</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="n">seed</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span>
<span class="c"># Train a naive Bayes model.</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">NaiveBayes</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="mf">1.0</span><span class="p">)</span>
<span class="c"># Make prediction and test accuracy.</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="o">.</span><span class="n">features</span><span class="p">),</span> <span class="n">p</span><span class="o">.</span><span class="n">label</span><span class="p">))</span>
<span class="n">accuracy</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="n">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span> <span class="n">x</span> <span class="o">==</span> <span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> <span class="o">/</span> <span class="n">test</span><span class="o">.</span><span class="n">count</span><span class="p">()</span></code></pre></div>
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