Github user sethah commented on a diff in the pull request:
https://github.com/apache/spark/pull/10639#discussion_r49395627
--- Diff: mllib/src/main/scala/org/apache/spark/ml/optim/GLMFamilies.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.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
+
+ /** Weights for IRLS steps. */
+ def weights(mu: Double): Double
+
+ /** 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 weights(mu: Double): Double = {
+ mu * (1 - mu)
--- End diff --
Hard coding the weights like this here won't be correct if anything other
than the canonical link function is used, I believe. Since we aren't doing
anything to restrict link functions to only the canonical ones, this should
probably defined in terms of the link function's derivative. Statsmodels does
it
[here](https://github.com/statsmodels/statsmodels/blob/master/statsmodels/genmod/families/family.py#L120).
---
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