[GitHub] spark pull request #14547: [SPARK-16718][MLlib] gbm-style treeboost

[facaiy <gi...@git.apache.org>]

Github user facaiy commented on a diff in the pull request:

    https://github.com/apache/spark/pull/14547#discussion_r105576961
  
    --- 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 --
    
    Hi,
    sum((p_i, y_i) in leaf) is confusing, as it is not appropriate format in LaTex.
    
    How about:
    L = sum_{x_i in leaf} 2 log(1 + exp(-2 y_i (p_i + gamma))) , where gamma = F(x_i) ?


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