Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/7278#discussion_r34304484
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/stat/test/ADTest.scala ---
@@ -0,0 +1,264 @@
+/*
+ * 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))}
+ }
+ }
+
+ /**
+ * 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 = math.log(y)
+ val b = math.log(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
--- End diff --
Why do you create an `Array` and convert to `iterator`? `pResult` will have
type `Double, Double, Double` here so can't we just return that?
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