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 --
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