Github user sryza commented on a diff in the pull request: https://github.com/apache/spark/pull/7075#discussion_r36125839 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/stat/test/KolmogorovSmirnovTest.scala --- @@ -190,5 +191,104 @@ private[stat] object KolmogorovSmirnovTest extends Logging { val pval = 1 - new CommonMathKolmogorovSmirnovTest().cdf(ksStat, n.toInt) new KolmogorovSmirnovTestResult(pval, ksStat, NullHypothesis.OneSampleTwoSided.toString) } + + /** + * Implements a two-sample, two-sided Kolmogorov-Smirnov test, which tests if the 2 samples + * come from the same distribution + * @param data1 `RDD[Double]` first sample of data + * @param data2 `RDD[Double]` second sample of data + * @return [[org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult]] with the test + * statistic, p-value, and appropriate null hypothesis + */ + def testTwoSamples(data1: RDD[Double], data2: RDD[Double]): KolmogorovSmirnovTestResult = { + val n1 = data1.count().toDouble + val n2 = data2.count().toDouble + // identifier for sample 1, needed after co-sort + val isSample1 = true + // combine identified samples + val unionedData = data1.map((_, isSample1)).union(data2.map((_, !isSample1))) + // co-sort and operate on each partition, returning local extrema to the driver + val localData = unionedData.sortByKey().mapPartitions( + searchTwoSampleCandidates(_, n1, n2) + ).collect() + // result: global extreme + val ksStat = searchTwoSampleStatistic(localData, n1 * n2) + evalTwoSampleP(ksStat, n1.toInt, n2.toInt) + } + + /** + * Calculates maximum distance candidates and counts of elements from each sample within one + * partition for the two-sample, two-sided Kolmogorov-Smirnov test implementation + * @param partData `Iterator[(Double, Boolean)]` the data in 1 partition of the co-sorted RDDs, + * each element is additionally tagged with a boolean flag for sample 1 membership + * @param n1 `Double` sample 1 size + * @param n2 `Double` sample 2 size + * @return `Iterator[(Double, Double, Double)]` where the first element is an unadjusted minimum + * distance, the second is an unadjusted maximum distance (both of which will later + * be adjusted by a constant to account for elements in prior partitions), and the third is + * a count corresponding to the numerator of the adjustment constant coming from this + * partition. This last value, the numerator of the adjustment constant, is calculated as + * |sample 2| * |sample 1 in partition| - |sample 1| * |sample 2 in partition|. This comes + * from the fact that when we adjust for prior partitions, what we are doing is + * adding the difference of the fractions (|prior elements in sample 1| / |sample 1| - + * |prior elements in sample 2| / |sample 2|). We simply keep track of the numerator + * portion that is attributable to each partition so that following partitions can + * use it to cumulatively adjust their values. + */ + private def searchTwoSampleCandidates( + partData: Iterator[(Double, Boolean)], + n1: Double, + n2: Double): Iterator[(Double, Double, Double)] = { + // fold accumulator: local minimum, local maximum, index for sample 1, index for sample2 + case class ExtremaAndIndices(min: Double, max: Double, ix1: Int, ix2: Int) + val initAcc = ExtremaAndIndices(Double.MaxValue, Double.MinValue, 0, 0) + // traverse the data in the partition and calculate distances and counts + val pResults = partData.foldLeft(initAcc) { case (acc, (v, isSample1)) => + val (add1, add2) = if (isSample1) (1, 0) else (0, 1) + val cdf1 = (acc.ix1 + add1) / n1 + val cdf2 = (acc.ix2 + add2) / n2 + val dist = cdf1 - cdf2 + ExtremaAndIndices( + math.min(acc.min, dist), + math.max(acc.max, dist), + acc.ix1 + add1, acc.ix2 + add2) + } + val results = if (pResults == initAcc) { --- End diff -- Can you provide a comment on what situations we would expect to hit this case in?
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