Github user yanboliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/15394#discussion_r84433100
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/optim/NormalEquationSolver.scala ---
@@ -0,0 +1,153 @@
+/*
+ * 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.ml.optim
+
+import breeze.linalg.{DenseVector => BDV}
+import breeze.optimize.{CachedDiffFunction, DiffFunction, LBFGS =>
BreezeLBFGS, OWLQN => BreezeOWLQN}
+import scala.collection.mutable
+
+import org.apache.spark.ml.linalg.{BLAS, DenseVector, Vectors}
+import org.apache.spark.mllib.linalg.CholeskyDecomposition
+
+private[ml] class NormalEquationSolution(
+ val coefficients: Array[Double],
+ val aaInv: Option[Array[Double]],
+ val objectiveHistory: Option[Array[Double]])
+
+/**
+ * Interface for classes that solve the normal equations locally.
+ */
+private[ml] sealed trait NormalEquationSolver {
+
+ /** Solve the normal equations from summary statistics. */
+ def solve(
+ bBar: Double,
+ bbBar: Double,
+ abBar: DenseVector,
+ aaBar: DenseVector,
+ aBar: DenseVector): NormalEquationSolution
+}
+
+/**
+ * A class that solves the normal equations directly, using Cholesky
decomposition.
+ */
+private[ml] class CholeskySolver extends NormalEquationSolver {
+
+ def solve(
+ bBar: Double,
+ bbBar: Double,
+ abBar: DenseVector,
+ aaBar: DenseVector,
+ aBar: DenseVector): NormalEquationSolution = {
+ val k = abBar.size
+ val x = CholeskyDecomposition.solve(aaBar.values, abBar.values)
+ val aaInv = CholeskyDecomposition.inverse(aaBar.values, k)
+
+ new NormalEquationSolution(x, Some(aaInv), None)
+ }
+}
+
+/**
+ * A class for solving the normal equations using Quasi-Newton
optimization methods.
+ */
+private[ml] class QuasiNewtonSolver(
+ val fitIntercept: Boolean,
+ maxIter: Int,
+ tol: Double,
+ l1RegFunc: Option[(Int) => Double]) extends NormalEquationSolver {
+
+ def solve(
+ bBar: Double,
+ bbBar: Double,
+ abBar: DenseVector,
+ aaBar: DenseVector,
+ aBar: DenseVector): NormalEquationSolution = {
+ val numFeatures = aBar.size
+ val numFeaturesPlusIntercept = if (fitIntercept) numFeatures + 1 else
numFeatures
+ val initialCoefficientsWithIntercept = new
Array[Double](numFeaturesPlusIntercept)
+ if (fitIntercept) {
+ initialCoefficientsWithIntercept(numFeaturesPlusIntercept - 1) = bBar
+ }
+
+ val costFun =
+ new NormalEquationCostFun(bBar, bbBar, abBar, aaBar, aBar,
fitIntercept, numFeatures)
+ val optimizer = l1RegFunc.map { func =>
+ new BreezeOWLQN[Int, BDV[Double]](maxIter, 10, func, tol)
+ }.getOrElse(new BreezeLBFGS[BDV[Double]](maxIter, 10, tol))
+
+ val states = optimizer.iterations(new CachedDiffFunction(costFun),
+ new BDV[Double](initialCoefficientsWithIntercept))
+
+ val arrayBuilder = mutable.ArrayBuilder.make[Double]
+ var state: optimizer.State = null
+ while (states.hasNext) {
+ state = states.next()
+ arrayBuilder += state.adjustedValue
+ }
+ val x = state.x.toArray.clone()
+ new NormalEquationSolution(x, None, Some(arrayBuilder.result()))
+ }
+
+ /**
+ * NormalEquationCostFun implements Breeze's DiffFunction[T] for the
normal equation.
+ * It returns the loss and gradient with L2 regularization at a
particular point (coefficients).
+ * It's used in Breeze's convex optimization routines.
+ */
+ private class NormalEquationCostFun(
+ bBar: Double,
+ bbBar: Double,
+ ab: DenseVector,
+ aa: DenseVector,
+ aBar: DenseVector,
+ fitIntercept: Boolean,
+ numFeatures: Int) extends DiffFunction[BDV[Double]] {
+
+ private val numFeaturesPlusIntercept = if (fitIntercept) numFeatures +
1 else numFeatures
+
+ override def calculate(coefficients: BDV[Double]): (Double,
BDV[Double]) = {
+ val coef = Vectors.fromBreeze(coefficients).toDense
+ if (fitIntercept) {
+ var j = 0
+ var dotProd = 0.0
+ val coefValues = coef.values
+ val aBarValues = aBar.values
+ while (j < numFeatures) {
+ dotProd += coefValues(j) * aBarValues(j)
+ j += 1
+ }
+ coefValues(numFeatures) = bBar - dotProd
+ }
+ val aax = new DenseVector(new
Array[Double](numFeaturesPlusIntercept))
+ BLAS.dspmv(numFeaturesPlusIntercept, 1.0, aa, coef, 1.0, aax)
+ // loss = 1/2 (b^T W b - 2 x^T A^T W b + x^T A^T W A x)
+ val loss = 0.5 * bbBar - BLAS.dot(ab, coef) + 0.5 * BLAS.dot(coef,
aax)
+ // -gradient = A^T W A x - A^T W b
--- End diff --
Annotation typo? Should be ```gradient = A^T W A x - A^T W b```?
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