Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38775271
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/optim/WeightedLeastSquares.scala ---
@@ -0,0 +1,295 @@
+/*
+ * 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 com.github.fommil.netlib.LAPACK.{getInstance => lapack}
+import org.netlib.util.intW
+
+import org.apache.spark.Logging
+import org.apache.spark.mllib.linalg._
+import org.apache.spark.mllib.linalg.distributed.RowMatrix
+import org.apache.spark.rdd.RDD
+
+/**
+ * Model fitted by [[WeightedLeastSquares]].
+ * @param coefficients model coefficients
+ * @param intercept model intercept
+ */
+private[ml] class WeightedLeastSquaresModel(
+ val coefficients: DenseVector,
+ val intercept: Double) extends Serializable
+
+/**
+ * Weighted least squares solver via normal equation.
+ * Given weighted observations (w,,i,,, a,,i,,, b,,i,,), we use the
following weighted least squares
+ * formulation:
+ *
+ * min,,x,z,, 1/2 sum,,i,, w,,i,, (a,,i,,^T^ x + z - b,,i,,)^2^ / sum,,i,,
w_i
+ * + 1/2 lambda / delta sum,,j,, (sigma,,j,, x,,j,,)^2^,
+ *
+ * where lambda is the regularization parameter, and delta and sigma,,j,,
are controlled by
+ * [[standardizeLabel]] and [[standardizeFeatures]], respectively.
+ *
+ * Set [[regParam]] to 0.0 and turn off both [[standardizeFeatures]] and
[[standardizeLabel]] to
+ * match R's `lm`.
+ * Turn on [[standardizeLabel]] to match R's `glmnet`.
+ *
+ * @param fitIntercept whether to fit intercept. If false, z is 0.0.
+ * @param regParam L2 regularization parameter (lambda)
+ * @param standardizeFeatures whether to standardize features. If true,
sigma_,,j,, is the
+ * population standard deviation of the j-th
column of A. Otherwise,
+ * sigma,,j,, is 1.0.
+ * @param standardizeLabel whether to standardize label. If true, delta is
the population standard
+ * deviation of the label column b. Otherwise,
delta is 1.0.
+ */
+private[ml] class WeightedLeastSquares(
+ val fitIntercept: Boolean,
+ val regParam: Double,
+ val standardizeFeatures: Boolean,
+ val standardizeLabel: Boolean) extends Logging with Serializable {
+ import WeightedLeastSquares._
+
+ require(regParam >= 0.0, s"regParam cannot be negative: $regParam")
+ if (regParam == 0.0) {
+ logWarning("regParam is zero, which might cause numerical instability
and overfit.")
+ }
+
+ /**
+ * Creates a [[WeightedLeastSquaresModel]] from an RDD of [[Instance]]s.
+ */
+ def fit(instances: RDD[Instance]): WeightedLeastSquaresModel = {
+ val summary = instances.treeAggregate(new Aggregator)(_.add(_),
_.merge(_))
+ summary.validate()
+ logInfo(s"Number of instances: ${summary.count}.")
+ val triK = summary.triK
+ val bBar = summary.bBar
+ val bStd = summary.bStd
+ val aBar = summary.aBar
+ val aVar = summary.aVar
+ val abBar = summary.abBar
+ val aaBar = summary.aaBar
+ val aaValues = aaBar.values
+
+ if (fitIntercept) {
+ // shift centers
+ // A^T A - aBar aBar^T
+ RowMatrix.dspr(-1.0, aBar, aaValues)
+ // A^T b - bBar aBar
+ BLAS.axpy(-bBar, aBar, abBar)
+ }
+
+ // add regularization to diagonals
+ var i = 0
+ var j = 2
+ while (i < triK) {
+ var lambda = regParam
+ if (standardizeFeatures) {
+ lambda *= aVar(j - 2)
+ }
+ if (standardizeLabel) {
+ // TODO: handle the case when bStd = 0
+ lambda /= bStd
+ }
+ aaValues(i) += lambda
+ i += j
+ j += 1
+ }
+
+ val x = choleskySolve(aaBar.values, abBar)
+
+ // compute intercept
+ val intercept = if (fitIntercept) {
+ bBar - BLAS.dot(aBar, x)
+ } else {
+ 0.0
+ }
+
+ new WeightedLeastSquaresModel(x, intercept)
+ }
+
+ /**
+ * Solves a symmetric positive definite linear system via Cholesky
factorization.
+ * The input arguments are modified in-place to store the factorization
and the solution.
+ * @param A the upper triangular part of A
+ * @param bx right-hand side
+ * @return the solution vector
+ */
+ private def choleskySolve(A: Array[Double], bx: DenseVector):
DenseVector = {
+ val k = bx.size
+ val info = new intW(0)
+ lapack.dppsv("U", k, 1, A, bx.values, k, info)
+ val code = info.`val`
+ assert(code == 0, s"lapack.dpotrs returned $code.")
+ bx
+ }
+}
+
+private[ml] object WeightedLeastSquares {
+
+ /**
+ * Case class for weighted observations.
+ * @param w weight, must be positive
+ * @param a features
+ * @param b label
+ */
+ case class Instance(w: Double, a: Vector, b: Double) {
+ require(w >= 0.0, s"Weight cannot be negative: $w.")
+ }
+
+ /**
+ * Aggregator to provide necessary summary statistics for solving
[[WeightedLeastSquares]].
+ */
+ // TODO: consolidate aggregates for summary statistics
+ private class Aggregator extends Serializable {
+ var initialized: Boolean = false
+ var k: Int = _
+ var count: Long = _
+ var triK: Int = _
+ private var wSum: Double = _
+ private var wwSum: Double = _
+ private var bSum: Double = _
+ private var bbSum: Double = _
+ private var aSum: DenseVector = _
+ private var abSum: DenseVector = _
+ private var aaSum: DenseVector = _
+
+ private def init(k: Int): Unit = {
+ require(k <= 4096, "In order to take the normal equation approach
efficiently, " +
+ s"we set the max number of features to 4096 but got $k.")
+ this.k = k
+ triK = k * (k + 1) / 2
+ count = 0L
+ wSum = 0.0
+ wwSum = 0.0
+ bSum = 0.0
+ bbSum = 0.0
+ aSum = new DenseVector(Array.ofDim(k))
+ abSum = new DenseVector(Array.ofDim(k))
+ aaSum = new DenseVector(Array.ofDim(triK))
+ initialized = true
+ }
+
+ /**
+ * Adds an instance.
+ */
+ def add(instance: Instance): this.type = {
+ val Instance(w, a, b) = instance
+ val ak = a.size
+ if (!initialized) {
+ init(ak)
+ initialized = true
+ }
+ assert(ak == k, s"Dimension mismatch. Expect vectors of size $k but
got $ak.")
+ count += 1L
+ wSum += w
+ wwSum += w * w
+ bSum += w * b
+ bbSum += w * b * b
+ BLAS.axpy(w, a, aSum)
+ BLAS.axpy(w * b, a, abSum)
+ RowMatrix.dspr(w, a, aaSum.values)
+ this
+ }
+
+ /**
+ * Merges another [[Aggregator]].
+ */
+ def merge(other: Aggregator): this.type = {
+ if (!other.initialized) {
+ this
+ } else {
+ if (!initialized) {
--- End diff --
If `this` is not initialized but `other` is, can we just return `other`?
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