Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/6994#discussion_r34226869
--- 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.
--- End diff --
I would move this paragraph inside the method as implementation details, or
only keep a copy in `KSTest`. End users do not need to know it.
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