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+---
+layout: global
+title: <a href="mllib-guide.html">MLlib</a> - Naive Bayes
+---
+
+Naive Bayes 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. For more details, please visit the wikipedia page
+[Naive Bayes classifier](http://en.wikipedia.org/wiki/Naive_Bayes_classifier).
+
+In MLlib, we implemented multinomial naive Bayes, which is typically used for document
+classification. Within that context, each observation is a document, each feature represents a term,
+whose value is the frequency of the term. For its formulation, please visit the wikipedia page
+[Multinomial naive Bayes](http://en.wikipedia.org/wiki/Naive_Bayes_classifier#Multinomial_naive_Bayes)
+or the section
+[Naive Bayes text classification](http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html)
+from the book Introduction to Information
+Retrieval. [Additive smoothing](http://en.wikipedia.org/wiki/Lidstone_smoothing) can be used by
+setting the parameter $\lambda$ (default to $1.0$). For document classification, the input feature
+vectors are usually sparse. Please supply sparse vectors as input to take advantage of
+sparsity. Since the training data is only used once, it is not necessary to cache it.
+
+## Examples
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+[NaiveBayes](api/mllib/index.html#org.apache.spark.mllib.classification.NaiveBayes$) implements
+multinomial naive Bayes. It takes an RDD of
+[LabeledPoint](api/mllib/index.html#org.apache.spark.mllib.regression.LabeledPoint) and an optional
+smoothing parameter `lambda` as input, and output a
+[NaiveBayesModel](api/mllib/index.html#org.apache.spark.mllib.classification.NaiveBayesModel), which
+can be used for evaluation and prediction.
+
+{% highlight scala %}
+import org.apache.spark.mllib.classification.NaiveBayes
+
+val training: RDD[LabeledPoint] = ... // training set
+val test: RDD[LabeledPoint] = ... // test set
+
+val model = NaiveBayes.train(training, lambda = 1.0)
+val prediction = model.predict(test.map(_.features))
+
+val predictionAndLabel = prediction.zip(test.map(_.label))
+val accuracy = 1.0 * predictionAndLabel.filter(x => x._1 == x._2).count() / test.count()
+{% endhighlight %}
+</div>
+
+<div data-lang="java" markdown="1">
+
+[NaiveBayes](api/mllib/index.html#org.apache.spark.mllib.classification.NaiveBayes$) implements
+multinomial naive Bayes. It takes a Scala RDD of
+[LabeledPoint](api/mllib/index.html#org.apache.spark.mllib.regression.LabeledPoint) and an
+optionally smoothing parameter `lambda` as input, and output a
+[NaiveBayesModel](api/mllib/index.html#org.apache.spark.mllib.classification.NaiveBayesModel), which
+can be used for evaluation and prediction.
+
+{% highlight java %}
+import org.apache.spark.mllib.classification.NaiveBayes;
+
+JavaRDD<LabeledPoint> training = ... // training set
+JavaRDD<LabeledPoint> test = ... // test set
+
+NaiveBayesModel model = NaiveBayes.train(training.rdd(), 1.0);
+
+JavaRDD<Double> prediction = model.predict(test.map(new Function<LabeledPoint, Vector>() {
+    public Vector call(LabeledPoint p) {
+      return p.features();
+    }
+  })
+JavaPairRDD<Double, Double> predictionAndLabel = 
+  prediction.zip(test.map(new Function<LabeledPoint, Double>() {
+    public Double call(LabeledPoint p) {
+      return p.label();
+    }
+  })
+double accuracy = 1.0 * predictionAndLabel.filter(new Function<Tuple2<Double, Double>, Boolean>() {
+    public Boolean call(Tuple2<Double, Double> pl) {
+      return pl._1() == pl._2();
+    }
+  }).count() / test.count()
+{% endhighlight %}
+</div>
+
+<div data-lang="python" markdown="1">
+
+[NaiveBayes](api/pyspark/pyspark.mllib.classification.NaiveBayes-class.html) implements multinomial
+naive Bayes. It takes an RDD of
+[LabeledPoint](api/pyspark/pyspark.mllib.regression.LabeledPoint-class.html) and an optionally
+smoothing parameter `lambda` as input, and output a
+[NaiveBayesModel](api/pyspark/pyspark.mllib.classification.NaiveBayesModel-class.html), which can be
+used for evaluation and prediction.
+
+<!--- TODO: Make Python's example consistent with Scala's and Java's. --->
+{% highlight python %}
+from pyspark.mllib.regression import LabeledPoint
+from pyspark.mllib.classification import NaiveBayes
+
+# an RDD of LabeledPoint
+data = sc.parallelize([
+  LabeledPoint(0.0, [0.0, 0.0])
+  ... # more labeled points
+])
+
+# Train a naive Bayes model.
+model = NaiveBayes.train(data, 1.0)
+
+# Make prediction.
+prediction = model.predict([0.0, 0.0])
+{% endhighlight %}
+
+</div>
+</div>