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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