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Posted to reviews@spark.apache.org by mengxr <gi...@git.apache.org> on 2015/09/03 18:53:26 UTC
[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
GitHub user mengxr opened a pull request:
https://github.com/apache/spark/pull/8588
[WIP][SPARK-9834][MLLIB] implement weighted least squares via normal equation
This is a WIP. Please do not spend time on documentation or code style.
The goal is to have a weighted least squares implementation that can later provide R-like summary statistics and support IRLS.
I try to match the result from glmnet but I found it quite hard to figure out how it handles regularization.
@dbtsai
You can merge this pull request into a Git repository by running:
$ git pull https://github.com/mengxr/spark SPARK-9834
Alternatively you can review and apply these changes as the patch at:
https://github.com/apache/spark/pull/8588.patch
To close this pull request, make a commit to your master/trunk branch
with (at least) the following in the commit message:
This closes #8588
----
commit 34107aa9654d9a7418fc5db9a67de556efde42c1
Author: Xiangrui Meng <me...@databricks.com>
Date: 2015-09-03T07:24:43Z
implement weighted least squares via normal equation
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959015
--- 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(
--- End diff --
This might be used by other algorithms like log-linear model or Lp regression. We can discuss this later.
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137525352
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138673301
LGTM, did not check low level implementation
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Posted by AmplabJenkins <gi...@git.apache.org>.
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https://github.com/apache/spark/pull/8588#issuecomment-138657110
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https://github.com/apache/spark/pull/8588#issuecomment-138673406
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by asfgit <gi...@git.apache.org>.
Github user asfgit closed the pull request at:
https://github.com/apache/spark/pull/8588
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137538143
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
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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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137512428
[Test build #41977 has started](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/41977/consoleFull) for PR 8588 at commit [`34107aa`](https://github.com/apache/spark/commit/34107aa9654d9a7418fc5db9a67de556efde42c1).
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138652809
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137525357
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137537973
[Test build #41979 has finished](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/41979/console) for PR 8588 at commit [`c75ff92`](https://github.com/apache/spark/commit/c75ff923428052c68e43004f5f2488cf0b3d72dc).
* This patch **passes all tests**.
* This patch merges cleanly.
* This patch adds the following public classes _(experimental)_:
* ` case class Instance(w: Double, a: Vector, b: Double) `
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137655130
[Test build #41994 has finished](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/41994/console) for PR 8588 at commit [`1614f22`](https://github.com/apache/spark/commit/1614f2280603df92af049e6deb016cb1de768e80).
* This patch **passes all tests**.
* This patch merges cleanly.
* This patch adds the following public classes _(experimental)_:
* ` case class Instance(w: Double, a: Vector, b: Double) `
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959084
--- 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.")
--- End diff --
done
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137650754
[Test build #41994 has started](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/41994/consoleFull) for PR 8588 at commit [`1614f22`](https://github.com/apache/spark/commit/1614f2280603df92af049e6deb016cb1de768e80).
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137538139
Merged build finished. Test PASSed.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137650250
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137655182
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138673319
jenkins retest this please
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by dbtsai <gi...@git.apache.org>.
Github user dbtsai commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38772511
--- Diff: mllib/src/test/scala/org/apache/spark/ml/optim/WeightedLeastSquaresSuite.scala ---
@@ -0,0 +1,133 @@
+/*
+ * 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 org.apache.spark.SparkFunSuite
+import org.apache.spark.ml.optim.WeightedLeastSquares.Instance
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.mllib.util.TestingUtils._
+import org.apache.spark.rdd.RDD
+
+class WeightedLeastSquaresSuite extends SparkFunSuite with MLlibTestSparkContext {
+
+ private var instances: RDD[Instance] = _
+
+ override def beforeAll(): Unit = {
+ super.beforeAll()
+ /*
+ R code:
+
+A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
+b <- c(17, 19, 23, 29)
+w <- c(1, 2, 3, 4)
+ */
+ instances = sc.parallelize(Seq(
+ Instance(1.0, Vectors.dense(0.0, 5.0).toSparse, 17.0),
+ Instance(2.0, Vectors.dense(1.0, 7.0), 19.0),
+ Instance(3.0, Vectors.dense(2.0, 11.0), 23.0),
+ Instance(4.0, Vectors.dense(3.0, 13.0), 29.0)
+ ), 2)
+ }
+
+ test("WLS against lm") {
+ /*
+ R code:
+
+df <- as.data.frame(cbind(A, b))
+for (formula in c(b ~ . -1, b ~ .)) {
+ model <- lm(formula, data=df, weights=w)
+ print(as.vector(coef(model)))
+}
+
+[1] -3.727121 3.009983
+[1] 18.08 6.08 -0.60
+ */
+
+ val expected = Seq(
+ Vectors.dense(0.0, -3.727121, 3.009983),
+ Vectors.dense(18.08, 6.08, -0.60))
+
+ var idx = 0
+ for (fitIntercept <- Seq(false, true)) {
+ val wls = new WeightedLeastSquares(
+ fitIntercept, regParam = 0.0, standardizeFeatures = false, standardizeLabel = false)
--- End diff --
Do we need `standardizeLabel`? I think without regularization, with/without standardization will not change the solution.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959027
--- 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) {
+ init(other.k)
+ }
+ assert(k == other.k)
--- End diff --
done
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138771604
Merged into master. I will make follow-up PRs to do the refactoring.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138673377
Merged build triggered.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959031
--- 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
--- End diff --
SPARK-10490
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38774759
--- 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
--- End diff --
This contains the cost function solved by `ALS.LeastSquaresNESolver` (and duplicates the Cholesky `dppsv` solver); should we make a JIRA to refactor existing code to reuse this class?
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138683028
[Test build #42145 has finished](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/42145/console) for PR 8588 at commit [`c2ec746`](https://github.com/apache/spark/commit/c2ec746ab6e9aee84dc984c912ab4f0ee2b4e75e).
* This patch **passes all tests**.
* This patch merges cleanly.
* This patch adds the following public classes _(experimental)_:
* ` case class Instance(w: Double, a: Vector, b: Double) `
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137528926
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
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https://github.com/apache/spark/pull/8588#issuecomment-138657114
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138674766
[Test build #42145 has started](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/42145/consoleFull) for PR 8588 at commit [`c2ec746`](https://github.com/apache/spark/commit/c2ec746ab6e9aee84dc984c912ab4f0ee2b4e75e).
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959092
--- 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 --
The contract of `merge` in Spark is that the first argument is mutable but not the second. See https://github.com/apache/spark/blob/master/core/src/main/scala/org/apache/spark/rdd/RDD.scala#L1068.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959002
--- Diff: mllib/src/test/scala/org/apache/spark/ml/optim/WeightedLeastSquaresSuite.scala ---
@@ -0,0 +1,133 @@
+/*
+ * 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 org.apache.spark.SparkFunSuite
+import org.apache.spark.ml.optim.WeightedLeastSquares.Instance
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.mllib.util.TestingUtils._
+import org.apache.spark.rdd.RDD
+
+class WeightedLeastSquaresSuite extends SparkFunSuite with MLlibTestSparkContext {
+
+ private var instances: RDD[Instance] = _
+
+ override def beforeAll(): Unit = {
+ super.beforeAll()
+ /*
+ R code:
+
+A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
+b <- c(17, 19, 23, 29)
+w <- c(1, 2, 3, 4)
+ */
+ instances = sc.parallelize(Seq(
+ Instance(1.0, Vectors.dense(0.0, 5.0).toSparse, 17.0),
+ Instance(2.0, Vectors.dense(1.0, 7.0), 19.0),
+ Instance(3.0, Vectors.dense(2.0, 11.0), 23.0),
+ Instance(4.0, Vectors.dense(3.0, 13.0), 29.0)
+ ), 2)
+ }
+
+ test("WLS against lm") {
+ /*
+ R code:
+
+df <- as.data.frame(cbind(A, b))
+for (formula in c(b ~ . -1, b ~ .)) {
+ model <- lm(formula, data=df, weights=w)
+ print(as.vector(coef(model)))
+}
+
+[1] -3.727121 3.009983
+[1] 18.08 6.08 -0.60
+ */
+
+ val expected = Seq(
+ Vectors.dense(0.0, -3.727121, 3.009983),
+ Vectors.dense(18.08, 6.08, -0.60))
+
+ var idx = 0
+ for (fitIntercept <- Seq(false, true)) {
+ val wls = new WeightedLeastSquares(
+ fitIntercept, regParam = 0.0, standardizeFeatures = false, standardizeLabel = false)
--- End diff --
We don't need it but I think it is useful to list the values explicitly here.
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137527221
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137655181
Merged build finished. Test PASSed.
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by SparkQA <gi...@git.apache.org>.
Github user SparkQA commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137525040
[Test build #41977 has finished](https://amplab.cs.berkeley.edu/jenkins/job/SparkPullRequestBuilder/41977/console) for PR 8588 at commit [`34107aa`](https://github.com/apache/spark/commit/34107aa9654d9a7418fc5db9a67de556efde42c1).
* This patch **passes all tests**.
* This patch merges cleanly.
* This patch adds the following public classes _(experimental)_:
* ` case class Instance(w: Double, a: Vector, b: Double) `
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-138683182
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by mengxr <gi...@git.apache.org>.
Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38959020
--- Diff: mllib/src/test/scala/org/apache/spark/ml/optim/WeightedLeastSquaresSuite.scala ---
@@ -0,0 +1,133 @@
+/*
+ * 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 org.apache.spark.SparkFunSuite
+import org.apache.spark.ml.optim.WeightedLeastSquares.Instance
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.mllib.util.TestingUtils._
+import org.apache.spark.rdd.RDD
+
+class WeightedLeastSquaresSuite extends SparkFunSuite with MLlibTestSparkContext {
+
+ private var instances: RDD[Instance] = _
+
+ override def beforeAll(): Unit = {
+ super.beforeAll()
+ /*
+ R code:
+
+A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
--- End diff --
This is actually easy for copying the code around. But I will update the indentation.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38774976
--- 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.")
--- End diff --
nit: "overfitting"
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137511010
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38773848
--- Diff: mllib/src/test/scala/org/apache/spark/ml/optim/WeightedLeastSquaresSuite.scala ---
@@ -0,0 +1,133 @@
+/*
+ * 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 org.apache.spark.SparkFunSuite
+import org.apache.spark.ml.optim.WeightedLeastSquares.Instance
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.mllib.util.TestingUtils._
+import org.apache.spark.rdd.RDD
+
+class WeightedLeastSquaresSuite extends SparkFunSuite with MLlibTestSparkContext {
+
+ private var instances: RDD[Instance] = _
+
+ override def beforeAll(): Unit = {
+ super.beforeAll()
+ /*
+ R code:
+
+A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
--- End diff --
The existing R code has usually been aligned with the `/*`
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by dbtsai <gi...@git.apache.org>.
Github user dbtsai commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38772704
--- 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(
--- End diff --
Will you merge this code into current `LinearRegression.scala`?
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[GitHub] spark pull request: [WIP][SPARK-9834][MLLIB] implement weighted le...
Posted by AmplabJenkins <gi...@git.apache.org>.
Github user AmplabJenkins commented on the pull request:
https://github.com/apache/spark/pull/8588#issuecomment-137527241
Merged build started.
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[GitHub] spark pull request: [SPARK-9834][MLLIB] implement weighted least s...
Posted by feynmanliang <gi...@git.apache.org>.
Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/8588#discussion_r38773970
--- 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) {
+ init(other.k)
+ }
+ assert(k == other.k)
--- End diff --
nit: this is missing an assertion error
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