Github user sryza commented on a diff in the pull request:
https://github.com/apache/spark/pull/7278#discussion_r35344727
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/stat/test/AndersonDarlingTest.scala
---
@@ -0,0 +1,289 @@
+/*
+ * 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 scala.annotation.varargs
+
+import collection.immutable.ListMap
+
+import org.apache.commons.math3.distribution.{ExponentialDistribution,
GumbelDistribution,
+ LogisticDistribution, NormalDistribution, WeibullDistribution}
+
+import org.apache.spark.Logging
+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 repeated values occur (the presence of ties can affect
the validity of the test).
+ * The AD test provides an alternative to the KS 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
+ * {{{
+ * A^2 = -N - \frac{1}{N}\sum_{i = 0}^{N} (2i + 1)(\ln{\Phi{(x_i)}} +
\ln{(1 - \Phi{(x_{N+1-i})})
+ * }}}
+ * where {{{\Phi}}} is the CDF of the given distribution and `N` is the
sample size.
+ * For more information
@see[[https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test]]
+ */
+private[stat] object AndersonDarlingTest extends Logging {
+
+ object NullHypothesis extends Enumeration {
+ type NullHypothesis = Value
+ val OneSample = Value("Sample follows theoretical distribution.")
+ }
+
+ /**
+ * AndersonDarlingTheoreticalDist 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 AndersonDarlingTheoreticalDist extends Serializable {
+ val params: Seq[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
+ }
+
+ /**
+ * Critical values and adjustments for distributions 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]],
which in turn
+ * references:
+ *
+ * Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and
+ * Some Comparisons, Journal of the American Statistical Association,
+ * Vol. 69, pp. 730-737.
+ *
+ * Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit
+ * Statistics with Unknown Parameters, Annals of Statistics, Vol. 4,
+ * pp. 357-369.
+ *
+ * Stephens, M. A. (1977). Goodness of Fit for the Extreme Value
+ * Distribution, Biometrika, Vol. 64, pp. 583-588.
+ *
+ * Stephens, M. A. (1977). Goodness of Fit with Special Reference
+ * to Tests for Exponentiality , Technical Report No. 262,
+ * Department of Statistics, Stanford University, Stanford, CA.
+ *
+ * Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution
+ * Based on the Empirical Distribution Function, Biometrika, Vol. 66,
+ * pp. 591-595.
+ */
+
+ // Exponential distribution
+ class AndersonDarlingExponential(val params: Seq[Double]) extends
AndersonDarlingTheoreticalDist {
+ 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 AndersonDarlingNormal(val params: Seq[Double]) extends
AndersonDarlingTheoreticalDist {
+ 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 AndersonDarlingGumbel(val params: Seq[Double]) extends
AndersonDarlingTheoreticalDist {
+ 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 AndersonDarlingLogistic(val params: Seq[Double]) extends
AndersonDarlingTheoreticalDist {
+ 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 AndersonDarlingWeibull(val params: Seq[Double]) extends
AndersonDarlingTheoreticalDist {
+ 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)) }
+ }
+ }
+
+ /**
+ * Perform a one sample Anderson-Darling test
+ * @param data data to test for a given distribution
+ * @param distName name of theoretical distribution: currently supports
normal,
+ * exponential, gumbel, logistic, weibull as
+ * ['norm', 'exp', 'gumbel', 'logistic', 'weibull']
+ * @param params variable-length argument providing parameters for given
distribution. When none
+ * are provided, default parameters appropriate to each
distribution are chosen. In
+ * either case, critical values reflect adjustments that
assume the parameters were
+ * estimated from the data
+ * @return
+ */
+ @varargs
+ def testOneSample(data: RDD[Double], distName: String, params: Double*)
+ : AndersonDarlingTestResult = {
+ val n = data.count()
+ val dist = initDist(distName, params)
+ val localData = data.sortBy(x => x).mapPartitions(calcPartAD(_, dist,
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 = dist.getCVs(n)
+ new AndersonDarlingTestResult(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
--- End diff --
Should this read "prior partition*s*"?
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