scala - Apache Spark - 两个样本 Kolmogorov-Smirnov 测试

Question

我在 Spark 中有两组数据(我们称它们为 d1、d2)。我想执行两个样本柯尔莫哥洛夫-斯米尔诺夫检验，以测试它们的底层总体分布函数是否不同。 MLLib 的 Statistics.kolmogorovSmirnovTest 可以做到这一点吗？

文档提供了这个示例:

import org.apache.spark.mllib.stat.Statistics

val data: RDD[Double] = ... // an RDD of sample data

// perform a KS test using a cumulative distribution function of our making
val myCDF: Double => Double = ...
val testResult2 = Statistics.kolmogorovSmirnovTest(data, myCDF)

我尝试计算 d2 的经验累积分布函数(将其收集为 Map)并将其与 d1 进行比较。

Statistics.kolmogorovSmirnovTest(d1, ecdf_map)

测试运行，但结果错误。

我做错了什么吗？是否有可能做到这一点？有什么想法吗？

感谢您的帮助!

Answer 1

在 Spark Mllib KolmogorovSmirnovTest是单采样且双面的。因此，如果您想要特定的两个采样变体，则在该库中是不可能的。但是，您仍然可以通过计算经验累积分布函数(我找到了一个库来执行此操作，因此如果结果良好，我将更新此答案)或使用正态分布的偏差来比较数据集。在此示例中，我将选择后者。

将 KST 统计数据与正态分布的数据集进行比较

为了进行此测试，我生成了 3 个发行版:2 triangular看起来相似，并且 exponential统计数据显示出巨大差异。

Note: I couldn't find any scientific papers describing this method as viable for distribution comparison so the idea is mostly empirical.

For every distribution you most definetely could find a mirrored one with the same global maximum distance between its CDF and normal distribution.

下一步是根据给定均值和标准差的正态分布获取 KS 结果。我将它们可视化以获得更好的图片:

如您所见，三角分布的结果(KS 统计数据和 p 值)彼此接近，而指数分布则相差很远。正如我在注释中所述，您可以通过镜像数据集轻松欺骗此方法，但对于真实世界的数据来说，这可能没问题。

import org.apache.spark._
import org.apache.spark.rdd.RDD
import org.apache.spark.mllib.stat.Statistics

import org.apache.commons.math3.distribution.{ ExponentialDistribution, TriangularDistribution }

import breeze.plot._
import breeze.linalg._
import breeze.numerics._

object Main {

    def main( args: Array[ String ] ): Unit = {

        val conf = 
            new SparkConf()
            .setAppName( "SO Spark" )
            .setMaster( "local[*]" )
            .set( "spark.driver.host", "localhost" )

        val sc = new SparkContext( conf )

        // Create similar distributions
        val triDist1 = new TriangularDistribution( -3, 5, 7 )
        val triDist2 = new TriangularDistribution( -3, 7, 7 )

        // Exponential distribution to show big difference
        val expDist1 = new ExponentialDistribution( 0.6 )

        // Sample data from the distributions and parallelize it
        val n = 100000
        val sampledTriDist1 = sc.parallelize( triDist1.sample( n ) )
        val sampledTriDist2 = sc.parallelize( triDist2.sample( n ) )
        val sampledExpDist1 = sc.parallelize( expDist1.sample( n ) )

        // KS tests
        val resultTriDist1 = Statistics
            .kolmogorovSmirnovTest( sampledTriDist1, 
                                    "norm", 
                                    sampledTriDist1.mean, 
                                    sampledTriDist1.stdev )

        val resultTriDist2 = Statistics
            .kolmogorovSmirnovTest( sampledTriDist2, 
                                    "norm", 
                                    sampledTriDist2.mean, 
                                    sampledTriDist2.stdev )

        val resultExpDist1 = Statistics
            .kolmogorovSmirnovTest( sampledExpDist1, 
                                    "norm", 
                                    sampledExpDist1.mean, 
                                    sampledExpDist1.stdev )

        // Results
        val statsTriDist1 = 
            "Tri1: ( " + 
            resultTriDist1.statistic + 
            ", " + 
            resultTriDist1.pValue + 
            " )"

        val statsTriDist2 = 
            "Tri2: ( " + 
            resultTriDist2.statistic + 
            ", " + 
            resultTriDist2.pValue + 
            " )"

        val statsExpDist1 = 
            "Exp1: ( " + 
            resultExpDist1.statistic + 
            ", " + 
            resultExpDist1.pValue + 
            " )"  

        println( statsTriDist1 )
        println( statsTriDist2 )
        println( statsExpDist1 )

        // Visualize
        val graphCanvas = Figure()

        val mainPlot = 
            graphCanvas
            .subplot( 0 )

        mainPlot.legend = true

        val x = linspace( 1, n, n )      

        mainPlot += plot( x, 
                          sampledTriDist1.sortBy( x => x ).take( n ), 
                          name = statsTriDist1 )

        mainPlot += plot( x, 
                          sampledTriDist2.sortBy( x => x ).take( n ), 
                          name = statsTriDist2 )

        mainPlot += plot( x, 
                          sampledExpDist1.sortBy( x => x ).take( n ), 
                          name = statsExpDist1 )

        mainPlot.xlabel = "x"
        mainPlot.ylabel = "sorted sample"

        mainPlot.title = "KS results for 2 Triangular and 1 Exponential Distributions"

        graphCanvas.saveas( "ks-sample.png", 300 )

        sc.stop()
    }
}