Github user sethah commented on a diff in the pull request:
https://github.com/apache/spark/pull/10639#discussion_r49618064
--- Diff: mllib/src/main/scala/org/apache/spark/ml/optim/GLMFamilies.scala
---
@@ -0,0 +1,138 @@
+/*
+ * 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.rdd.RDD
+
+/**
+ * A description of the error distribution and link function to be used in
the model.
+ * @param link a link function instance
+ */
+private[ml] abstract class Family(val link: Link) extends Serializable {
+
+ /**
+ * Starting value for mu in the IRLS algorithm.
+ */
+ def startingMu(y: Double, yMean: Double): Double = (y + yMean) / 2.0
+
+ /**
+ * Deviance of (y, mu) pair.
+ * Deviance is usually defined as twice the loglikelihood ratio.
+ */
+ def deviance(y: RDD[Double], mu: RDD[Double]): Double
+
+ /** The variance of mu to its mean. */
+ def variance(mu: Double): Double = 1.0
+
+ /** Weights for IRLS steps. */
+ def weights(mu: Double): Double = {
+ 1.0 / (math.pow(this.link.deriv(mu), 2.0) * this.variance(mu))
+ }
+
+ /** The adjusted response variable. */
+ def adjusted(y: Double, mu: Double, eta: Double): Double = {
+ eta + (y - mu) * link.deriv(mu)
+ }
+
+ /** Linear predictors based on given mu. */
+ def predict(mu: Double): Double = this.link.link(mu)
+
+ /** Fitted values based on linear predictors eta. */
+ def fitted(eta: Double): Double = this.link.unlink(eta)
+}
+
+/**
+ * Binomial exponential family distribution.
+ * The default link for the Binomial family is the logit link.
+ * @param link a link function instance
+ */
+private[ml] class Binomial(link: Link = Logit) extends Family(link) {
+
+ override def startingMu(y: Double, yMean: Double): Double = (y + 0.5) /
2.0
+
+ override def deviance(y: RDD[Double], mu: RDD[Double]): Double = {
+ mu.zip(y).map { case (mu, y) =>
+ val my = 1.0 - y
+ y * math.log(math.max(y, 1.0) / mu) +
+ my * math.log(math.max(my, 1.0) / (1.0 - mu))
+ }.sum() * 2
+ }
+
+ override def variance(mu: Double): Double = {
+ mu * (1 - mu)
+ }
+}
+
+private[ml] object Binomial {
+
+ def apply(link: Link): Binomial = new Binomial(link)
+}
+
+/**
+ * Poisson exponential family.
+ * The default link for the Poisson family is the log link.
+ * @param link a link function instance
+ */
+private[ml] class Poisson(link: Link = Log) extends Family(link) {
+
+ override def deviance(y: RDD[Double], mu: RDD[Double]): Double = {
+ mu.zip(y).map { case (mu, y) =>
+ y * math.log(math.max(y, 1.0) / mu) - (y - mu)
--- End diff --
Is there a reference you can point to for this exact form of the deviance
equation (other than SparkGLM package)? I haven't seen the max function in
other places.
This may or may not be related, but how will we guarantee that the
endogenous variable does not contain invalid values (negative for poisson,
outside [0, 1] for binomial, etc...?
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