Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/916#discussion_r13613361
--- Diff:
core/src/main/scala/org/apache/spark/util/random/SamplingUtils.scala ---
@@ -0,0 +1,50 @@
+/*
+ * 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.util.random
+
+private[spark] object SamplingUtils {
+
+ /**
+ * 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),
+ * 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.
+ *
+ * @param num sample size
+ * @param total size of RDD
+ * @param withReplacement whether sampling with replacement
+ * @return a sampling rate that guarantees sufficient sample size with
99.99% success rate
+ */
+ def computeFraction(num: Int, total: Long, withReplacement: Boolean):
Double = {
--- End diff --
Let's give it a more descriptive name, e.g.,
`computeFractionForLeastSampleSize`. You may have a better name.
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