Github user mengxr commented on a diff in the pull request: https://github.com/apache/spark/pull/6994#discussion_r34226872 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/stat/Statistics.scala --- @@ -158,4 +158,47 @@ object Statistics { def chiSqTest(data: RDD[LabeledPoint]): Array[ChiSqTestResult] = { ChiSqTest.chiSquaredFeatures(data) } + + /** + * 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. + * @param data an `RDD[Double]` containing the sample of data to test + * @param cdf a `Double => Double` function to calculate the theoretical CDF at a given value + * @return KSTestResult object containing test statistic, p-value, and null hypothesis. --- End diff -- link `KSTestResult`
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