Github user sryza commented on a diff in the pull request:
https://github.com/apache/spark/pull/6994#discussion_r33515526
--- 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:
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
--- End diff --
indent these two spaces
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