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Check sample size and move computeFraction
Check that the sample size is within supported range. Moved computeFraction int a private util class in util.random
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core/src/main/scala/org/apache/spark/util/random/SamplingUtils.scala
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| /* | ||
| * 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. | ||
| */ | ||
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| package org.apache.spark.util.random | ||
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| private[spark] object SamplingUtils { | ||
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| /** | ||
| * 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 = { | ||
| val fraction = num.toDouble / total | ||
| if (withReplacement) { | ||
| val numStDev = if (num < 12) 9 else 5 | ||
| fraction + numStDev * math.sqrt(fraction / total) | ||
| } else { | ||
| val delta = 1e-4 | ||
| val gamma = - math.log(delta) / total | ||
| math.min(1, fraction + gamma + math.sqrt(gamma * gamma + 2 * gamma * fraction)) | ||
| } | ||
| } | ||
| } |
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core/src/test/scala/org/apache/spark/util/random/SamplingUtilsSuite.scala
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| /* | ||
| * 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. | ||
| */ | ||
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| package org.apache.spark.util.random | ||
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| import org.apache.commons.math3.distribution.{BinomialDistribution, PoissonDistribution} | ||
| import org.scalatest.FunSuite | ||
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| class SamplingUtilsSuite extends FunSuite{ | ||
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| test("computeFraction") { | ||
| // test that the computed fraction guarantees enough datapoints | ||
| // in the sample with a failure rate <= 0.0001 | ||
| val n = 100000 | ||
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| for (s <- 1 to 15) { | ||
| val frac = SamplingUtils.computeFraction(s, n, true) | ||
| val poisson = new PoissonDistribution(frac * n) | ||
| assert(poisson.inverseCumulativeProbability(0.0001) >= s, "Computed fraction is too low") | ||
| } | ||
| for (s <- List(20, 100, 1000)) { | ||
| val frac = SamplingUtils.computeFraction(s, n, true) | ||
| val poisson = new PoissonDistribution(frac * n) | ||
| assert(poisson.inverseCumulativeProbability(0.0001) >= s, "Computed fraction is too low") | ||
| } | ||
| for (s <- List(1, 10, 100, 1000)) { | ||
| val frac = SamplingUtils.computeFraction(s, n, false) | ||
| val binomial = new BinomialDistribution(n, frac) | ||
| assert(binomial.inverseCumulativeProbability(0.0001)*n >= s, "Computed fraction is too low") | ||
| } | ||
| } | ||
| } |