Github user mengxr commented on a diff in the pull request: https://github.com/apache/spark/pull/3519#discussion_r23594894 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/regression/IsotonicRegression.scala --- @@ -0,0 +1,238 @@ +/* + * 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.mllib.regression + +import java.io.Serializable +import java.util.Arrays.binarySearch + +import org.apache.spark.api.java.{JavaDoubleRDD, JavaRDD} +import org.apache.spark.rdd.RDD + +/** + * Regression model for Isotonic regression + * + * @param features Array of features. + * @param labels Array of labels associated to the features at the same index. + */ +class IsotonicRegressionModel ( + features: Array[Double], + val labels: Array[Double]) + extends Serializable { + + /** + * Predict labels for provided features + * Using a piecewise constant function + * + * @param testData features to be labeled + * @return predicted labels + */ + def predict(testData: RDD[Double]): RDD[Double] = + testData.map(predict) + + /** + * Predict labels for provided features + * Using a piecewise constant function + * + * @param testData features to be labeled + * @return predicted labels + */ + def predict(testData: JavaRDD[java.lang.Double]): JavaDoubleRDD = + JavaDoubleRDD.fromRDD(predict(testData.rdd.asInstanceOf[RDD[Double]])) + + /** + * Predict a single label + * Using a piecewise constant function + * + * @param testData feature to be labeled + * @return predicted label + */ + def predict(testData: Double): Double = { + val result = binarySearch(features, testData) + + val index = + if (result == -1) { + 0 + } else if (result < 0) { + -result - 2 + } else { + result + } + + labels(index) + } +} + +/** + * Isotonic regression + * Currently implemented using parallel pool adjacent violators algorithm + */ +class IsotonicRegression + extends Serializable { + + /** + * Run algorithm to obtain isotonic regression model + * + * @param input (label, feature, weight) + * @param isotonic isotonic (increasing) or antitonic (decreasing) sequence + * @return isotonic regression model + */ + def run( + input: RDD[(Double, Double, Double)], + isotonic: Boolean = true): IsotonicRegressionModel = { + createModel( + parallelPoolAdjacentViolators(input, isotonic), + isotonic) + } + + /** + * Creates isotonic regression model with given parameters + * + * @param predictions labels estimated using isotonic regression algorithm. + * Used for predictions on new data points. + * @param isotonic isotonic (increasing) or antitonic (decreasing) sequence + * @return isotonic regression model + */ + protected def createModel( + predictions: Array[(Double, Double, Double)], + isotonic: Boolean): IsotonicRegressionModel = { + + val labels = predictions.map(_._1) + val features = predictions.map(_._2) + + new IsotonicRegressionModel(features, labels) + } + + /** + * Performs a pool adjacent violators algorithm (PAVA) + * Uses approach with single processing of data where violators + * in previously processed data created by pooling are fixed immediatelly. + * Uses optimization of discovering monotonicity violating sequences (blocks) + * Method in situ mutates input array + * + * @param in input data + * @param isotonic asc or desc + * @return result + */ + private def poolAdjacentViolators( + in: Array[(Double, Double, Double)], + isotonic: Boolean): Array[(Double, Double, Double)] = { + + // Pools sub array within given bounds assigning weighted average value to all elements + def pool(in: Array[(Double, Double, Double)], start: Int, end: Int): Unit = { + val poolSubArray = in.slice(start, end + 1) + + val weightedSum = poolSubArray.map(lp => lp._1 * lp._3).sum + val weight = poolSubArray.map(_._3).sum + + var i = start + while (i <= end) { + in(i) = (weightedSum / weight, in(i)._2, in(i)._3) + i = i + 1 + } + } + + val monotonicityConstraintHolds: (Double, Double) => Boolean = + (x, y) => if (isotonic) x <= y else x >= y + + var i = 0 + while (i < in.length) { + var j = i + + // Find monotonicity violating sequence, if any + while (j < in.length - 1 && !monotonicityConstraintHolds(in(j)._1, in(j + 1)._1)) { + j = j + 1 + } + + // If monotonicity was not violated, move to next data point + if (i == j) { + i = i + 1 + } else { + // Otherwise pool the violating sequence + // And check if pooling caused monotonicity violation in previously processed points + while (i >= 0 && !monotonicityConstraintHolds(in(i)._1, in(i + 1)._1)) { + pool(in, i, j) + i = i - 1 + } + + i = j + } + } + + in + } + + /** + * Performs parallel pool adjacent violators algorithm + * Calls Pool adjacent violators on each partition and then again on the result + * + * @param testData input + * @param isotonic isotonic (increasing) or antitonic (decreasing) sequence + * @return result --- End diff -- ... and the result.
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