Github user facaiy commented on a diff in the pull request:
https://github.com/apache/spark/pull/14547#discussion_r105814881
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/tree/impurity/ApproxBernoulliImpurity.scala
---
@@ -0,0 +1,155 @@
+/*
+ * 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.tree.impurity
+
+import org.apache.spark.annotation.{DeveloperApi, Since}
+import org.apache.spark.mllib.tree.impurity._
+
+/**
+ * [[ApproxBernoulliImpurity]] currently uses variance as a (proxy)
impurity measure
+ * during tree construction. The main purpose of the class is to have an
alternative
+ * leaf prediction calculation.
+ *
+ * Only data with examples each of weight 1.0 is supported.
+ *
+ * Class for calculating variance during regression.
+ */
+@Since("2.1")
+private[spark] object ApproxBernoulliImpurity extends Impurity {
+
+ /**
+ * :: DeveloperApi ::
+ * information calculation for multiclass classification
+ * @param counts Array[Double] with counts for each label
+ * @param totalCount sum of counts for all labels
+ * @return information value, or 0 if totalCount = 0
+ */
+ @Since("2.1")
+ @DeveloperApi
+ override def calculate(counts: Array[Double], totalCount: Double):
Double =
+ throw new
UnsupportedOperationException("ApproxBernoulliImpurity.calculate")
+
+ /**
+ * :: DeveloperApi ::
+ * variance calculation
+ * @param count number of instances
+ * @param sum sum of labels
+ * @param sumSquares summation of squares of the labels
+ * @return information value, or 0 if count = 0
+ */
+ @Since("2.1")
+ @DeveloperApi
+ override def calculate(count: Double, sum: Double, sumSquares: Double):
Double = {
+ Variance.calculate(count, sum, sumSquares)
+ }
+}
+
+/**
+ * Class for updating views of a vector of sufficient statistics,
+ * in order to compute impurity from a sample.
+ * Note: Instances of this class do not hold the data; they operate on
views of the data.
+ */
+private[spark] class ApproxBernoulliAggregator
+ extends ImpurityAggregator(statsSize = 4) with Serializable {
+
+ /**
+ * Update stats for one (node, feature, bin) with the given label.
+ * @param allStats Flat stats array, with stats for this (node,
feature, bin) contiguous.
+ * @param offset Start index of stats for this (node, feature, bin).
+ */
+ def update(allStats: Array[Double], offset: Int, label: Double,
instanceWeight: Double): Unit = {
+ allStats(offset) += instanceWeight
+ allStats(offset + 1) += instanceWeight * label
+ allStats(offset + 2) += instanceWeight * label * label
+ allStats(offset + 3) += instanceWeight * Math.abs(label)
+ }
+
+ /**
+ * Get an [[ImpurityCalculator]] for a (node, feature, bin).
+ * @param allStats Flat stats array, with stats for this (node,
feature, bin) contiguous.
+ * @param offset Start index of stats for this (node, feature, bin).
+ */
+ def getCalculator(allStats: Array[Double], offset: Int):
ApproxBernoulliCalculator = {
+ new ApproxBernoulliCalculator(allStats.view(offset, offset +
statsSize).toArray)
+ }
+}
+
+/**
+ * Stores statistics for one (node, feature, bin) for calculating impurity.
+ * Unlike [[ImpurityAggregator]], this class stores its own data and is
for a specific
+ * (node, feature, bin).
+ * @param stats Array of sufficient statistics for a (node, feature, bin).
+ */
+private[spark] class ApproxBernoulliCalculator(stats: Array[Double])
+ extends ImpurityCalculator(stats) {
+
+ require(stats.length == 4,
+ s"ApproxBernoulliCalculator requires sufficient statistics array stats
to be of length 4," +
+ s" but was given array of length ${stats.length}.")
+
+ /**
+ * Make a deep copy of this [[ImpurityCalculator]].
+ */
+ def copy: ApproxBernoulliCalculator = new
ApproxBernoulliCalculator(stats.clone())
+
+ /**
+ * Calculate the impurity from the stored sufficient statistics.
+ */
+ def calculate(): Double = ApproxBernoulliImpurity.calculate(stats(0),
stats(1), stats(2))
+
+ /**
+ * Number of data points accounted for in the sufficient statistics.
+ */
+ def count: Long = stats(0).toLong
+
+ /**
+ * Prediction which should be made based on the sufficient statistics.
+ */
+ def predict: Double = if (count == 0) {
+ 0
+ } else {
+ // Per Friedman 1999, we use a single Newton-Raphson step from gamma =
0 to find the
+ // optimal leaf prediction, the solution gamma to the minimization
problem:
+ // L = sum((p_i, y_i) in leaf) 2 log(1 + exp(-2 y_i (p_i + gamma)))
--- End diff --
By the way,
how about the explanation without knowing of Newton's optimization?
as:
gamma = \argmin L
= \argmin sum_{x_i in leaf} 2 log(1 + exp(-2 y_i (p_i +
gamma)))
= 2 \argmin sum_{x_i in leaf} log(1 + exp(-2 y_i (p_i +
gamma)))
= \argmin sum_{x_i in leaf} log(1 + exp(-2 y_i (p_i +
gamma)))
= original formula (Eq. 23) in Friedman paper
namely,
the optimal value of gamma is not affected by 2 in our LogLoss definition.
However, as our gradient y' of LogLoss is -2 times than \slide{y} (Eq.
22): y' = -2 \slide{y}
hence, the final formula need be modified as:
r_jm = \sum y' / ( 2 \sum |y'| - \sum y'^2 / 2 )
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