Github user HyukjinKwon commented on a diff in the pull request:
https://github.com/apache/spark/pull/16013#discussion_r89676784
--- Diff:
core/src/main/scala/org/apache/spark/util/random/SamplingUtils.scala ---
@@ -67,20 +67,23 @@ private[spark] object SamplingUtils {
}
/**
- * Returns a sampling rate that guarantees a sample of size >=
sampleSizeLowerBound 99.99% of
- * the time.
+ * Returns a sampling rate that guarantees a sample of size greater than
or equal to
+ * sampleSizeLowerBound 99.99% of the time.
*
* How the sampling rate is determined:
+ *
+ * {{{
* Let p = num / total, where num is the sample size and total is the
total number of
* datapoints in the RDD. We're trying to compute q > p such that
- * - when sampling with replacement, we're drawing each datapoint with
prob_i ~ Pois(q),
- * where we want to guarantee Pr[s < num] < 0.0001 for s =
sum(prob_i for i from 0 to total),
+ * - when sampling with replacement, we're drawing each datapoint with
prob_i ~ Pois(q), where
+ * we want to guarantee Pr[s < num] < 0.0001 for s = sum(prob_i for
i from 0 to total),
* i.e. the failure rate of not having a sufficiently large sample <
0.0001.
* Setting q = p + 5 * sqrt(p/total) is sufficient to guarantee
0.9999 success rate for
* num > 12, but we need a slightly larger q (9 empirically
determined).
* - when sampling without replacement, we're drawing each datapoint
with prob_i
* ~ Binomial(total, fraction) and our choice of q guarantees
1-delta, or 0.9999 success
* rate, where success rate is defined the same as in sampling with
replacement.
+ * }}}
--- End diff --
- Java
<img width="790" alt="2016-11-27 4 35 27"
src="https://cloud.githubusercontent.com/assets/6477701/20642763/01760360-b45b-11e6-9d6f-9753baa54a37.png";>
Scaladoc not found
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