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mllib/src/main/scala/org/apache/spark/ml/optim/IterativelyReweightedLeastSquares.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.ml.optim | ||
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import org.apache.spark.Logging | ||
import org.apache.spark.ml.feature.Instance | ||
import org.apache.spark.mllib.linalg._ | ||
import org.apache.spark.rdd.RDD | ||
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/** | ||
* Model fitted by [[IterativelyReweightedLeastSquares]]. | ||
* @param coefficients model coefficients | ||
* @param intercept model intercept | ||
*/ | ||
private[ml] class IterativelyReweightedLeastSquaresModel( | ||
val coefficients: DenseVector, | ||
val intercept: Double) extends Serializable | ||
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/** | ||
* Implements the method of iteratively reweighted least squares (IRLS) which is used to solve | ||
* certain optimization problems by an iterative method. In each step of the iterations, it | ||
* involves solving a weighted lease squares (WLS) problem by [[WeightedLeastSquares]]. | ||
* It can be used to find maximum likelihood estimates of a generalized linear model (GLM), | ||
* find M-estimator in robust regression and other optimization problems. | ||
* | ||
* @param initialModel the initial guess model. | ||
* @param reweightFunc the reweight function which is used to update offsets and weights | ||
* at each iteration. | ||
* @param fitIntercept whether to fit intercept. | ||
* @param regParam L2 regularization parameter used by WLS. | ||
* @param maxIter maximum number of iterations. | ||
* @param tol the convergence tolerance. | ||
* | ||
* @see [[http://www.jstor.org/stable/2345503 P. J. Green, Iteratively Reweighted Least Squares | ||
* for Maximum Likelihood Estimation, and some Robust and Resistant Alternatives, | ||
* Journal of the Royal Statistical Society. Series B, 1984.]] | ||
*/ | ||
private[ml] class IterativelyReweightedLeastSquares( | ||
val initialModel: WeightedLeastSquaresModel, | ||
val reweightFunc: (Instance, WeightedLeastSquaresModel) => (Double, Double), | ||
val fitIntercept: Boolean, | ||
val regParam: Double, | ||
val maxIter: Int, | ||
val tol: Double) extends Logging with Serializable { | ||
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def fit(instances: RDD[Instance]): IterativelyReweightedLeastSquaresModel = { | ||
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var converged = false | ||
var iter = 0 | ||
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var model: WeightedLeastSquaresModel = initialModel | ||
var oldModel: WeightedLeastSquaresModel = null | ||
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while (iter < maxIter && !converged) { | ||
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oldModel = model | ||
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// Update offsets and weights using reweightFunc | ||
val newInstances = instances.map { instance => | ||
val (newOffset, newWeight) = reweightFunc(instance, oldModel) | ||
Instance(newOffset, newWeight, instance.features) | ||
} | ||
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// Estimate new model | ||
model = new WeightedLeastSquares(fitIntercept, regParam, standardizeFeatures = false, | ||
standardizeLabel = false).fit(newInstances) | ||
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// Check convergence | ||
val oldCoefficients = oldModel.coefficients | ||
val coefficients = model.coefficients | ||
BLAS.axpy(-1.0, coefficients, oldCoefficients) | ||
val maxTolOfCoefficients = oldCoefficients.toArray.reduce { (x, y) => | ||
math.max(math.abs(x), math.abs(y)) | ||
} | ||
val maxTol = math.max(maxTolOfCoefficients, math.abs(oldModel.intercept - model.intercept)) | ||
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if (maxTol < tol) { | ||
converged = true | ||
logInfo(s"IRLS converged in $iter iterations.") | ||
} | ||
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logInfo(s"Iteration $iter : relative tolerance = $maxTol") | ||
iter = iter + 1 | ||
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if (iter == maxIter) { | ||
logInfo(s"IRLS reached the max number of iterations: $maxIter.") | ||
} | ||
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} | ||
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new IterativelyReweightedLeastSquaresModel(model.coefficients, model.intercept) | ||
} | ||
} |
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