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From josepablocam <...@git.apache.org>
Subject [GitHub] spark pull request: [SPARK-8598] [MLlib] Implementation of 1-sampl...
Date Thu, 09 Jul 2015 01:13:05 GMT
Github user josepablocam commented on a diff in the pull request:

    https://github.com/apache/spark/pull/6994#discussion_r34215935
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/stat/test/KSTest.scala ---
    @@ -0,0 +1,191 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one or more
    + * contributor license agreements.  See the NOTICE file distributed with
    + * this work for additional information regarding copyright ownership.
    + * The ASF licenses this file to You under the Apache License, Version 2.0
    + * (the "License"); you may not use this file except in compliance with
    + * the License.  You may obtain a copy of the License at
    + *
    + *    http://www.apache.org/licenses/LICENSE-2.0
    + *
    + * Unless required by applicable law or agreed to in writing, software
    + * distributed under the License is distributed on an "AS IS" BASIS,
    + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    + * See the License for the specific language governing permissions and
    + * limitations under the License.
    + */
    +
    +package org.apache.spark.mllib.stat.test
    +
    +import org.apache.commons.math3.distribution.{NormalDistribution, RealDistribution}
    +import org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest
    +
    +import org.apache.spark.rdd.RDD
    +
    +/**
    + * Conduct the two-sided Kolmogorov Smirnov test for data sampled from a
    + * continuous distribution. By comparing the largest difference between the empirical
cumulative
    + * distribution of the sample data and the theoretical distribution we can provide a
test for the
    + * the null hypothesis that the sample data comes from that theoretical distribution.
    + * For more information on KS Test:
    + * @see [[https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test]]
    + *
    + * Implementation note: We seek to implement the KS test with a minimal number of distributed
    + * passes. We sort the RDD, and then perform the following operations on a per-partition
basis:
    + * calculate an empirical cumulative distribution value for each observation, and a theoretical
    + * cumulative distribution value. We know the latter to be correct, while the former
will be off by
    + * a constant (how large the constant is depends on how many values precede it in other
partitions).
    + * However, given that this constant simply shifts the ECDF upwards, but doesn't change
its shape,
    + * and furthermore, that constant is the same within a given partition, we can pick 2
values
    + * in each partition that can potentially resolve to the largest global distance. Namely,
we
    + * pick the minimum distance and the maximum distance. Additionally, we keep track of
how many
    + * elements are in each partition. Once these three values have been returned for every
partition,
    + * we can collect and operate locally. Locally, we can now adjust each distance by the
appropriate
    + * constant (the cumulative sum of # of elements in the prior partitions divided by the
data set
    + * size). Finally, we take the maximum absolute value, and this is the statistic.
    + */
    +private[stat] object KSTest {
    +
    +  // Null hypothesis for the type of KS test to be included in the result.
    +  object NullHypothesis extends Enumeration {
    +    type NullHypothesis = Value
    +    val oneSampleTwoSided = Value("Sample follows theoretical distribution.")
    +  }
    +
    +  /**
    +   * Runs a KS test for 1 set of sample data, comparing it to a theoretical distribution
    +   * @param data `RDD[Double]` data on which to run test
    +   * @param cdf `Double => Double` function to calculate the theoretical CDF
    +   * @return KSTestResult summarizing the test results (pval, statistic, and null hypothesis)
    +   */
    +  def testOneSample(data: RDD[Double], cdf: Double => Double): KSTestResult = {
    +    val n = data.count().toDouble
    +    val localData = data.sortBy(x => x).mapPartitions { part =>
    +      val partDiffs = oneSampleDifferences(part, n, cdf) // local distances
    +      searchOneSampleCandidates(partDiffs) // candidates: local extrema
    +    }.collect()
    +    val ksStat = searchOneSampleStatistic(localData, n) // result: global extreme
    +    evalOneSampleP(ksStat, n.toLong)
    +  }
    +
    +  /**
    +   * Runs a KS test for 1 set of sample data, comparing it to a theoretical distribution
    +   * @param data `RDD[Double]` data on which to run test
    +   * @param createDist `Unit => RealDistribution` function to create a theoretical
distribution
    +   * @return KSTestResult summarizing the test results (pval, statistic, and null hypothesis)
    +   */
    +  def testOneSample(data: RDD[Double], createDist: () => RealDistribution): KSTestResult
= {
    +    val n = data.count().toDouble
    +    val localData = data.sortBy(x => x).mapPartitions { part =>
    +      val partDiffs = oneSampleDifferences(part, n, createDist) // local distances
    +      searchOneSampleCandidates(partDiffs) // candidates: local extrema
    +    }.collect()
    +    val ksStat = searchOneSampleStatistic(localData, n) // result: global extreme
    +    evalOneSampleP(ksStat, n.toLong)
    +  }
    +
    +  /**
    +   * Calculate unadjusted distances between the empirical CDF and the theoretical CDF
in a
    +   * partition
    +   * @param partData `Iterator[Double]` 1 partition of a sorted RDD
    +   * @param n `Double` the total size of the RDD
    +   * @param cdf `Double => Double` a function the calculates the theoretical CDF of
a value
    +   * @return `Iterator[(Double, Double)] `Unadjusted (ie. off by a constant) potential
extrema
    +   *        in a partition. The first element corresponds to the (ECDF - 1/N) - CDF,
the second
    +   *        element corresponds to ECDF - CDF.  We can then search the resulting iterator
    +   *        for the minimum of the first and the maximum of the second element, and provide
this
    +   *        as a partition's candidate extrema
    +   */
    +  private def oneSampleDifferences(partData: Iterator[Double], n: Double, cdf: Double
=> Double)
    +    : Iterator[(Double, Double)] = {
    +    // zip data with index (within that partition)
    +    // calculate local (unadjusted) ECDF and subtract CDF
    +    partData.zipWithIndex.map { case (v, ix) =>
    +      // dp and dl are later adjusted by constant, when global info is available
    +      val dp = (ix + 1) / n
    +      val dl = ix / n
    +      val cdfVal = cdf(v)
    +      (dl - cdfVal, dp - cdfVal)
    +    }
    +  }
    +
    +  private def oneSampleDifferences(
    +      partData: Iterator[Double],
    +      n: Double,
    +      createDist: () => RealDistribution)
    +    : Iterator[(Double, Double)] = {
    +    val dist = createDist()
    +    oneSampleDifferences(partData, n, x => dist.cumulativeProbability(x))
    +  }
    +
    +  /**
    +   * Search the unadjusted differences in a partition and return the
    +   * two extrema (furthest below and furthest above CDF), along with a count of elements
in that
    +   * partition
    +   * @param partDiffs `Iterator[(Double, Double)]` the unadjusted differences between
ECDF and CDF
    +   *                 in a partition, which come as a tuple of (ECDF - 1/N - CDF, ECDF
- CDF)
    +   * @return `Iterator[(Double, Double, Double)]` the local extrema and a count of elements
    +   */
    +  private def searchOneSampleCandidates(partDiffs: Iterator[(Double, Double)])
    +    : Iterator[(Double, Double, Double)] = {
    +    val initAcc = (Double.MaxValue, Double.MinValue, 0.0)
    +    val pResults = partDiffs.foldLeft(initAcc) { case ((pMin, pMax, pCt), (dl, dp)) =>
    +      (math.min(pMin, dl), math.max(pMax, dp), pCt + 1)
    +    }
    +    val results = if (pResults == initAcc) Array[(Double, Double, Double)]() else Array(pResults)
    +    results.iterator
    +  }
    +
    +  /**
    +   * Find the global maximum distance between ECDF and CDF (i.e. the KS Statistic) after
adjusting
    +   * local extrema estimates from individual partitions with the amount of elements in
preceding
    +   * partitions
    +   * @param localData `Array[(Double, Double, Double)]` A local array containing the
collected
    +   *                 results of `searchOneSampleCandidates` across all partitions
    +   * @param n `Double`The size of the RDD
    +   * @return The one-sample Kolmogorov Smirnov Statistic
    +   */
    +  private def searchOneSampleStatistic(localData: Array[(Double, Double, Double)], n:
Double)
    +    : Double = {
    +    val initAcc = (Double.MinValue, 0.0)
    +    // adjust differences based on the # of elements preceding it, which should provide
    +    // the correct distance between ECDF and CDF
    +    val results = localData.foldLeft(initAcc) { case ((prevMax, prevCt), (minCand, maxCand,
ct)) =>
    +      val adjConst = prevCt / n
    +      val dist1 = math.abs(minCand + adjConst)
    +      val dist2 = math.abs(maxCand + adjConst)
    +      val maxVal = Array(prevMax, dist1, dist2).max
    +      (maxVal, prevCt + ct)
    +    }
    +    results._1
    +  }
    +
    +  /**
    +   * A convenience function that allows running the KS test for 1 set of sample data
against
    +   * a named distribution
    +   * @param data the sample data that we wish to evaluate
    +   * @param distName the name of the theoretical distribution
    +   * @param params Variable length parameter for distribution's parameters
    +   * @return KSTestResult summarizing the test results (pval, statistic, and null hypothesis)
    +   */
    +  def testOneSample(data: RDD[Double], distName: String, params: Double*): KSTestResult
= {
    +    val distanceCalc =
    +      distName match {
    +        case "norm" => () => {
    +          require(params.length == 2, "Normal distribution requires mean and standard
" +
    --- End diff --
    
    Added


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