/* 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 io.github.mandar2812.dynaml.optimization import breeze.linalg._ import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.rdd.RDD import scala.util.Random /** * @author mandar2812 */ class ConjugateGradientSpark extends RegularizedOptimizer[DenseVector[Double], DenseVector[Double], Double, RDD[LabeledPoint]]{ def getRegParam = this.regParam def getFeatureMatrix(nPoints: Long, ParamOutEdges: RDD[LabeledPoint], initialP: DenseVector[Double], frac: Double, regParam: Double) = { val dims = initialP.length //Cast as problem of form A.w = b //A = Phi^T . Phi + I_dims*regParam //b = Phi^T . Y val (a,b): (DenseMatrix[Double], DenseVector[Double]) = ParamOutEdges.filter((_) => Random.nextDouble() <= frac) .mapPartitions((edges) => { Seq(edges.map((edge) => { val phi = DenseVector(edge.features.toArray) val label = edge.label val phiY: DenseVector[Double] = phi * label (phi*phi.t, phiY) }).reduce((couple1, couple2) => { (couple1._1+couple2._1, couple1._2+couple2._2) })).toIterator }).reduce((couple1, couple2) => { (couple1._1+couple2._1, couple1._2+couple2._2) }) (a,b) } /** * Find the optimum value of the parameters using * Gradient Descent. * * @param nPoints The number of data points * @param initialP The initial value of the parameters * as a [[DenseVector]] * @param ParamOutEdges An [[java.lang.Iterable]] object * having all of the out edges of the * parameter node * * @return The value of the parameters as a [[DenseVector]] * * * */ override def optimize(nPoints: Long, ParamOutEdges: RDD[LabeledPoint], initialP: DenseVector[Double]): DenseVector[Double] = { val (a,b) = getFeatureMatrix(nPoints, ParamOutEdges, initialP, this.miniBatchFraction, this.regParam) val smoother:DenseMatrix[Double] = DenseMatrix.eye[Double](initialP.length)/this.regParam smoother(-1,-1) = 0.0 ConjugateGradient.runCG(a+smoother, b, initialP, 0.0001, this.numIterations) } } object ConjugateGradientSpark { /** * Solves for x in A.x = b (where A is symmetric +ve semi-definite) * iteratively using the Conjugate Gradient * algorithm. * */ def runCG(A: DenseMatrix[Double], b: DenseVector[Double], x: DenseVector[Double], epsilon: Double, MAX_ITERATIONS: Int): DenseVector[Double] = { val residual = b - (A*x) val p = residual var count = 1.0 var alpha = math.pow(norm(residual, 2), 2)/(p.t * (A*p)) var beta = 0.0 while(norm(residual, 2) >= epsilon && count <= MAX_ITERATIONS) { //update x axpy(alpha, p, x) //before updating residual, calculate norm (required for beta) val de = math.pow(norm(residual, 2), 2) //update residual axpy(-1.0*alpha, A*p, residual) //calculate beta beta = math.pow(norm(residual, 2), 2)/de //update p p :*= beta axpy(1.0, residual, p) //update alpha alpha = math.pow(norm(residual, 2), 2)/(p.t * (A*p)) count += 1 } x } }