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From srowen <...@git.apache.org>
Subject [GitHub] spark pull request: [SPARK-8884] [MLlib] 1-sample Anderson-Darling...
Date Wed, 08 Jul 2015 10:03:11 GMT
Github user srowen commented on a diff in the pull request:

    https://github.com/apache/spark/pull/7278#discussion_r34132657
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/stat/test/ADTest.scala ---
    @@ -0,0 +1,269 @@
    +/*
    + * 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 collection.immutable.ListMap
    +
    +import org.apache.commons.math3.distribution.{ExponentialDistribution, GumbelDistribution,
    +  LogisticDistribution, NormalDistribution, WeibullDistribution}
    +
    +import org.apache.spark.rdd.RDD
    +
    +/**
    + * The Anderson Darling (AD) test, similarly to the Kolmogorov Smirnov (KS) test, tests
whether the
    + * data follow a given theoretical distribution. It should be used with continuous data
and
    + * assumes that no ties occur (the presence of ties can affect the validity of the test).
    + * The AD test provides an alternative to the Kolmogorov-Smirnov test. Namely, it is
better
    + * suited to identify departures from the theoretical distribution at the tails.
    + * It is worth noting that the the AD test's critical values depend on the
    + * distribution being tested against.
    + * The  AD statistic is defined as -n - s/n, where
    + * s = sum from i=1 to n of (2i + 1)(ln(z_i) + ln(1 - z_{n+1-i})
    + * where z_i is the CDF value of the ith observation in the sorted sample.
    + * For more information @see[[https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test]]
    + */
    +private[stat] object ADTest {
    +
    +  object NullHypothesis extends Enumeration {
    +    type NullHypothesis = Value
    +    val oneSample = Value("Sample follows theoretical distribution.")
    +  }
    +
    +  /**
    +   * ADTheoreticalDist is a trait that every distribution used in an AD test must extend.
    +   * The rationale for this is that the AD test has distribution-dependent critical values,
and by
    +   * requiring extension of this trait we guarantee that future additional distributions
    +   * make sure to add the appropriate critical values (CVs) (or at least acknowledge
    +   * that they should be added)
    +   */
    +  sealed trait ADTheoreticalDist {
    +    val params: Array[Double]  // parameters used to initialized the distribution
    +
    +    def cdf(x: Double): Double // calculate the cdf under the given distribution for
value x
    +
    +    def getCVs(n: Double): Map[Double, Double] // return appropriate CVs, adjusted for
sample size
    +  }
    +
    +  /**
    +   * Sourced from
    +   * http://civil.colorado.edu/~balajir/CVEN5454/lectures/Ang-n-Tang-Chap7-Goodness-of-fit-PDFs-
    +   * test.pdf
    +   * https://github.com/scipy/scipy/blob/v0.15.1/scipy/stats/morestats.py#L1017
    +   */
    +
    +  // Exponential distribution
    +  class ADExponential(val params: Array[Double]) extends ADTheoreticalDist {
    +    private val theoretical = new ExponentialDistribution(params(0))
    +
    +    private val rawCVs = ListMap(
    +      0.15 -> 0.922, 0.10 -> 1.078,
    +      0.05 -> 1.341, 0.025 -> 1.606, 0.01 -> 1.957
    +    )
    +
    +    def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
    +
    +    def getCVs(n: Double): Map[Double, Double] = {
    +      rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.6 / n)}
    +    }
    +  }
    +
    +  // Normal Distribution
    +  class ADNormal(val params: Array[Double]) extends ADTheoreticalDist {
    +    private val theoretical = new NormalDistribution(params(0), params(1))
    +
    +    private val rawCVs = ListMap(
    +      0.15 -> 0.576, 0.10 -> 0.656,
    +      0.05 -> 0.787, 0.025 -> 0.918, 0.01 -> 1.092
    +    )
    +
    +    def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
    +
    +    def getCVs(n: Double): Map[Double, Double] = {
    +      rawCVs.map { case (sig, cv) => sig -> cv / (1 + 4.0 / n - 25.0 / (n * n))
}
    +    }
    +  }
    +
    +  // Gumbel distribution
    +  class ADGumbel(val params: Array[Double]) extends ADTheoreticalDist {
    +    private val theoretical = new GumbelDistribution(params(0), params(1))
    +
    +    private val rawCVs = ListMap(
    +      0.25 -> 0.474, 0.10 -> 0.637,
    +      0.05 -> 0.757, 0.025 -> 0.877, 0.01 -> 1.038
    +    )
    +
    +    def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
    +
    +    def getCVs(n: Double): Map[Double, Double] = {
    +      rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.2 / math.sqrt(n))}
    +    }
    +  }
    +
    +  // Logistic distribution
    +  class ADLogistic(val params: Array[Double]) extends ADTheoreticalDist {
    +    private val theoretical = new LogisticDistribution(params(0), params(1))
    +
    +    private val rawCVs = ListMap(
    +      0.25 -> 0.426, 0.10 -> 0.563, 0.05 -> 0.660,
    +      0.025 -> 0.769, 0.01 -> 0.906, 0.005 -> 1.010
    +    )
    +
    +    def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
    +
    +    def getCVs(n: Double): Map[Double, Double] = {
    +      rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.25 / n)}
    +    }
    +  }
    +
    +  // Weibull distribution
    +  class ADWeibull(val params: Array[Double]) extends ADTheoreticalDist {
    +    private val theoretical = new WeibullDistribution(params(0), params(1))
    +
    +    private val rawCVs = ListMap(
    +      0.25 -> 0.474, 0.10 -> 0.637,
    +      0.05 -> 0.757, 0.025 -> 0.877, 0.01 -> 1.038
    +    )
    +
    +    def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
    +
    +    def getCVs(n: Double): Map[Double, Double] = {
    +      rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.2 / math.sqrt(n))}
    +    }
    +  }
    +
    +  // math.log1p calculates ln(x + 1), so subtract 1
    +  private def ln(x: Double): Double = math.log1p(x - 1)
    +
    +  /**
    +   * Perform a one sample Anderson Darling test
    +   * @param data `RDD[Double]` data to test for a given distribution
    +   * @param distName `String` name of theoretical distribution: currently supports standard
normal,
    +   *            exponential, gumbel, logistic, weibull
    +   * @param params optional variable-length argument providing parameters for given distribution,
    +   *               otherwise they are estimated from sample but in both cases we adjust
critical
    +   *               values assuming they were estimated from sample. Providing them is
simply a
    +   *               convenience to avoid recalculation when the values are already available
to
    +   *               the user
    +   * @return Anderson-Darling test result
    +   */
    +  def testOneSample(data: RDD[Double], distName: String, params: Double*): ADTestResult
= {
    +    val n = data.count()
    +    val makeDist = initDist(distName, data, n, params.toArray)
    +    val localData = data.sortBy(x => x).mapPartitions(calcPartAD(_, makeDist, n)).collect()
    +    val s = localData.foldLeft((0.0, 0.0)) { case ((prevStat, prevCt), (rawStat, adj,
ct)) =>
    +        val adjVal = 2 * prevCt * adj
    +        val adjustedStat = rawStat + adjVal
    +        val cumCt = prevCt + ct
    +        (prevStat + adjustedStat, cumCt)
    +    }._1
    +    val ADStat = - 1 * n - s / n
    +    val criticalVals = makeDist().getCVs(n)
    +    new ADTestResult(ADStat, criticalVals, NullHypothesis.oneSample.toString)
    +  }
    +
    +
    +  /**
    +   * Calculate a partition's contribution to the Anderson Darling statistic.
    +   * In each partition we calculate 2 values, an unadjusted value that is contributed
to the AD
    +   * statistic directly, a value that must be adjusted by the number of values in the
prior
    +   * partition, and a count of the elements in that partition
    +   * @param part `Iterator[Double]` a partition of the data sample to be analyzed
    +   * @param makeDist `() => ADTheoreticalDist` a function to create a class that extends
the
    +   *                ADTheoreticalDist trait, which requires various methods, used in
creating 1
    +   *                object per partition
    +   * @param n `Double` the total size of the data sample
    +   * @return `Iterator[(Double, Double, Double)]` The first element corresponds to the
    +   *        position-independent contribution to the AD statistic, the second is the
value that must
    +   *        be scaled by the number of elements in prior partitions and the third is
the number of
    +   *        elements in this partition
    +   */
    +  def calcPartAD(part: Iterator[Double], makeDist: () => ADTheoreticalDist, n: Double)
    +    : Iterator[(Double, Double, Double)] = {
    +      val dist = makeDist()
    +      val initAcc = (0.0, 0.0, 0.0)
    +      val pResult = part.zipWithIndex.foldLeft(initAcc) { case ((prevS, prevC, prevCt),
(v, i)) =>
    +        val y = dist.cdf(v)
    +        val a = ln(y)
    +        val b = ln(1 - y)
    +        val unAdjusted = a * (2 * i + 1) + b * (2 * n - 2 * i - 1)
    +        val adjConstant = a - b
    +        (prevS + unAdjusted, prevC + adjConstant, prevCt + 1)
    +      }
    +    Array(pResult).iterator
    +  }
    +
    +  /**
    +   * Create a function to produce a distribution per partition.
    +   * If the user provides parameters, the distribution is initialized with those values
    +   * (note that the critical values still assume that the parameters were estimated from
the data,
    +   * the ability to provide the parameters is simply a convenience to avoid recomputing
them
    +   * when the user already has them available). If no parameters are provided, and the
distribution
    +   * is one of [normal, exponential], then the distribution is initialized with MLE values
    +   * @param distName `String` name of distribution
    +   * @param data `RDD[Double]` sample of data to analyze (and hence to use for parameter
estimation
    +   *            where possible)
    +   * @param n `Double` size of data sample
    +   * @param params `Double*` Initialization parameters for distribution
    +   * @return `() => RealDistribution` function to create distribution object
    +   */
    +  def initDist(distName: String, data: RDD[Double], n: Double, params: Array[Double])
    +    : () => ADTheoreticalDist = {
    +    distName match {
    +      case "norm" => {
    +        val muHat = if (params.nonEmpty) params(0) else data.mean()
    +        val sdHat = if (params.length > 1) {
    +            params(1)
    +          } else {
    +            math.sqrt(data.map(x => math.pow(x - muHat, 2)).sum() / (n - 1))
    +        }
    +        () => new ADNormal(Array(muHat, sdHat))
    +      }
    +      case "exp" => {
    +        val meanHat = if (params.nonEmpty) params(0) else data.mean()
    +        () => new ADExponential(Array(meanHat))
    +      }
    +      case "gumbel" => {
    +        if (params.length < 2) {
    +          throw new Exception("Gumbel does not yet support parameter estimation. " +
    --- End diff --
    
    You shouldn't throw raw Exception in general. Use `require` everywhere you need arg checking


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