贝叶斯、朴素贝叶斯及调用spark官网 mllib NavieBayes示例

贝叶斯法则

  机器学习的任务：在给定训练数据A时，肯定假设空间B中的最佳假设。

  最佳假设：一种方法是把它定义为在给定数据A以及B中不一样假设的先验几率的有关知识下的最可能假设

  贝叶斯理论提供了一种计算假设几率的方法，基于假设的先验几率、给定假设下观察到不一样数据的几率以及观察到的数据自己

先验几率和后验几率  

 用P(A)表示在没有训练数据前假设A拥有的初始几率。P(A)被称为A的先验几率。

 先验几率反映了关于A是一正确假设的机会的背景知识

 若是没有这一先验知识，能够简单地将每一候选假设赋予相同的先验几率

 相似地，P(B)表示训练数据B的先验几率，P(A|B)表示假设B成立时A的几率

 机器学习中，咱们关心的是P(B|A)，即给定A时B的成立的几率，称为B的后验几率

贝叶斯公式

 贝叶斯公式提供了从先验几率P(A)、P(B)和P(A|B)计算后验几率P(B|A)的方法

贝叶斯定理即是基于下述贝叶斯公式：

P(B|A)随着P(B)和P(A|B)的增加而增加，随着P(A)的增加而减小，即若是A独立于B时被观察到的可能性越大，那么A对B的支持度越小

朴素贝叶斯 

朴素贝叶斯算法是假设各个特征之间相互独立,使用贝叶斯公式进行分类的。请参考：https://blog.csdn.net/amds123/article/details/70173402 

 

spark NavieBayes 官方示例代码以下：

import org.apache.spark.ml.classification.NaiveBayes
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
import org.apache.spark.sql.SparkSession

object NavieBayesDemo {
  def main(args: Array[String]): Unit = {
    val spark = SparkSession
      .builder
      .appName("NavieBayesDemo").master("local")
      .config("spark.sql.warehouse.dir", "C:\\study\\sparktest")
      .getOrCreate()
    // Load the data stored in LIBSVM format as a DataFrame.
    val dataset=spark.read.format("libsvm").load("data/mllib/sample_libsvm_data.txt")
    // Split the data into training and test sets (30% held out for testing)
    val Array(tranningData,testData)=dataset.randomSplit(Array(0.7,0.3),seed = 1234L)

    // Train a NavieBayes model
    val model = new NaiveBayes().fit(tranningData)
    // Select example rows to display.
    val predictions=model.transform(testData)
    predictions.show()

    // Select (prediction, true label) and compute test error
    val evaluator = new MulticlassClassificationEvaluator()
      .setLabelCol("label")
      .setPredictionCol("prediction")
      .setMetricName("accuracy")
    val accuracy = evaluator.evaluate(predictions)
    println(s"Test set accuracy = $accuracy")
    
    spark.stop()
  }
}

运行结果以下：  

18/10/24 11:50:06 INFO SparkContext: Starting job: collectAsMap at MulticlassMetrics.scala:48

+-----+--------------------+--------------------+-----------+----------+

|label|            features|       rawPrediction|probability|prediction|

+-----+--------------------+--------------------+-----------+----------+

|  0.0|(692,[95,96,97,12...|[-173678.60946628...|  [1.0,0.0]|       0.0|

|  0.0|(692,[98,99,100,1...|[-178107.24302988...|  [1.0,0.0]|       0.0|

|  0.0|(692,[100,101,102...|[-100020.80519087...|  [1.0,0.0]|       0.0|

|  0.0|(692,[124,125,126...|[-183521.85526462...|  [1.0,0.0]|       0.0|

|  0.0|(692,[127,128,129...|[-183004.12461660...|  [1.0,0.0]|       0.0|

|  0.0|(692,[128,129,130...|[-246722.96394714...|  [1.0,0.0]|       0.0|

|  0.0|(692,[152,153,154...|[-208696.01108598...|  [1.0,0.0]|       0.0|

|  0.0|(692,[153,154,155...|[-261509.59951302...|  [1.0,0.0]|       0.0|

|  0.0|(692,[154,155,156...|[-217654.71748256...|  [1.0,0.0]|       0.0|

|  0.0|(692,[181,182,183...|[-155287.07585335...|  [1.0,0.0]|       0.0|

|  1.0|(692,[99,100,101,...|[-145981.83877498...|  [0.0,1.0]|       1.0|

|  1.0|(692,[100,101,102...|[-147685.13694275...|  [0.0,1.0]|       1.0|

|  1.0|(692,[123,124,125...|[-139521.98499849...|  [0.0,1.0]|       1.0|

|  1.0|(692,[124,125,126...|[-129375.46702012...|  [0.0,1.0]|       1.0|

|  1.0|(692,[126,127,128...|[-145809.08230799...|  [0.0,1.0]|       1.0|

|  1.0|(692,[127,128,129...|[-132670.15737290...|  [0.0,1.0]|       1.0|

|  1.0|(692,[128,129,130...|[-100206.72054749...|  [0.0,1.0]|       1.0|

|  1.0|(692,[129,130,131...|[-129639.09694930...|  [0.0,1.0]|       1.0|

|  1.0|(692,[129,130,131...|[-143628.65574273...|  [0.0,1.0]|       1.0|

|  1.0|(692,[129,130,131...|[-129238.74023248...|  [0.0,1.0]|       1.0|

+-----+--------------------+--------------------+-----------+----------+

only showing top 20 rows

18/10/24 11:50:06 INFO DAGScheduler: Job 6 finished: countByValue at MulticlassMetrics.scala:42, took 0.157446 s

Test set accuracy = 1.0