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From: tillrohrmann <git@git.apache.org>
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References: <git-pr-861-flink@git.apache.org>
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Subject: [GitHub] flink pull request: [FLINK-2030][FLINK-2274][ml]Online
 Histograms ...
Content-Type: text/plain
Message-Id: <20150820173423.6228CE7DD9@git1-us-west.apache.org>
Date: Thu, 20 Aug 2015 17:34:23 +0000 (UTC)

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

    https://github.com/apache/flink/pull/861#discussion_r37557444
  
    --- Diff: flink-staging/flink-ml/src/main/scala/org/apache/flink/ml/statistics/ContinuousHistogram.scala ---
    @@ -0,0 +1,315 @@
    +/*
    + * 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.flink.ml.statistics
    +
    +import scala.Double.MaxValue
    +import scala.collection.mutable
    +
    +/** Implementation of a continuous valued online histogram
    +  * Adapted from Ben-Haim and Yom-Tov's Streaming Decision Tree Algorithm
    +  * Refer http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf
    +  *
    +  * =Parameters=
    +  * -[[capacity]]:
    +  * Number of bins to be used in the histogram
    +  *
    +  * -[[min]]:
    +  * Lower limit on the elements
    +  *
    +  * -[[max]]:
    +  * Upper limit on the elements
    +  */
    +class ContinuousHistogram(capacity: Int, min: Double, max: Double) extends OnlineHistogram {
    +
    +  private val lower = min
    +  private val upper = max
    +
    +  require(capacity > 0, "Capacity should be a positive integer")
    +  require(lower < upper, "Lower must be less than upper")
    +
    +  val data = new mutable.ArrayBuffer[(Double, Int)]()
    +
    +  /** Adds a new item to the histogram
    +    *
    +    * @param p value to be added
    +    */
    +  override def add(p: Double): Unit = {
    +    require(p > lower && p < upper, p + " not in (" + lower + "," + upper + ")")
    +    // search for the index where the value is just higher than p
    +    val search = find(p)
    +    // add the new value there, shifting everything to the right
    +    data.insert(search, (p, 1))
    +    // If we're over capacity or any two elements are within 1e-9 of each other, merge.
    +    // This will take care of the case if p was actually equal to some value in the histogram and
    +    // just increment the value there
    +    mergeElements()
    +  }
    +
    +  /** Merges the histogram with h and returns a histogram with capacity B
    +    *
    +    * @param h histogram to be merged
    +    * @param B capacity of the resultant histogram
    +    * @return Merged histogram with capacity B
    +    */
    +  override def merge(h: OnlineHistogram, B: Int): ContinuousHistogram = {
    +    h match {
    +      case temp: ContinuousHistogram => {
    +        val m: Int = bins
    +        val n: Int = temp.bins
    +        var i, j: Int = 0
    +        val mergeList = new mutable.ArrayBuffer[(Double, Int)]()
    +        while (i < m || j < n) {
    +          if (i >= m) {
    +            mergeList += ((temp.getValue(j), temp.getCounter(j)))
    +            j = j + 1
    +          } else if (j >= n || getValue(i) <= temp.getValue(j)) {
    +            mergeList += data.apply(i)
    +            i = i + 1
    +          } else {
    +            mergeList += ((temp.getValue(j), temp.getCounter(j)))
    +            j = j + 1
    +          }
    +        }
    +        // the size will be brought to capacity while constructing the new histogram itself
    +        val finalLower = Math.min(lower, temp.lower)
    +        val finalUpper = Math.max(upper, temp.upper)
    +        val ret = new ContinuousHistogram(B, finalLower, finalUpper)
    +        ret.loadData(mergeList.toArray)
    +        ret
    +      }
    +      case default =>
    +        throw new RuntimeException("Only a continuous histogram is allowed to be merged with a " +
    +          "continuous histogram")
    +
    +    }
    +  }
    +
    +  /** Returns the qth quantile of the histogram
    +    *
    +    * @param q Quantile value in (0,1)
    +    * @return Value at quantile q
    +    */
    +  def quantile(q: Double): Double = {
    +    require(bins > 0, "Histogram is empty")
    +    require(q > 0 && q < 1, "Quantile must be between 0 and 1")
    +    val wantedSum = (q * total).round.toInt
    +    var currSum = count(getValue(0))
    +
    +    if (wantedSum < currSum) {
    +      require(lower > -MaxValue, "Set a lower bound before proceeding")
    +      return Math.sqrt(2 * wantedSum * Math.pow(getValue(0) - lower, 2) / getCounter(0)) + lower
    +    }
    +
    +    /** Walk the histogram to find sums at every bin value
    +      * As soon as you hit the interval where you should be
    +      * Walk along the trapezoidal line
    +      * This leads to solving a quadratic equation.
    +      */
    +    for (i <- 1 to bins - 1) {
    +      val tmpSum = count(getValue(i))
    +      if (currSum <= wantedSum && wantedSum < tmpSum) {
    +        val neededSum = wantedSum - currSum
    +        val a: Double = getCounter(i) - getCounter(i - 1)
    +        val b: Double = 2 * getCounter(i - 1)
    +        val c: Double = -2 * neededSum
    +        if (a == 0) {
    +          return getValue(i - 1) + (getValue(i) - getValue(i - 1)) * (-c / b)
    +        } else {
    +          return getValue(i - 1) +
    +            (getValue(i) - getValue(i - 1)) * (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a)
    +        }
    +      } else {
    +        currSum = tmpSum
    +      }
    +    }
    +    require(upper < MaxValue, "Set an upper bound before proceeding")
    +    // this means wantedSum > sum(getValue(bins-1))
    +    // this will likely fail to return a bounded value.
    +    // Make sure you set some proper limits on min and max.
    +    getValue(bins - 1) + Math.sqrt(
    +      Math.pow(upper - getValue(bins - 1), 2) * 2 * (wantedSum - currSum) / getCounter(bins - 1))
    +  }
    +
    +  /** Returns the probability (and by extension, the number of points) for the value b
    +    * Since this is a continuous histogram, return the cumulative probability at b
    +    *
    +    * @return Cumulative number of points at b
    +    */
    +  def count(b: Double): Int = {
    +    require(bins > 0, "Histogram is empty")
    +    if (b < lower) {
    +      return 0
    +    }
    +    if (b >= upper) {
    +      return total
    +    }
    +    /** Suppose x is the index with value just less than or equal to b
    +      * Then, sum everything up to x-1
    +      * Add half the value at x
    +      * Find area of the trapezoid for x and the value b
    +      */
    +
    +    val index = find(b) - 1
    +    var m_b, s: Double = 0
    +    if (index == -1) {
    +      m_b = getCounter(index + 1) * (b - lower) / (getValue(index + 1) - lower)
    +      s = m_b * (b - lower) / (2 * (getValue(index + 1) - lower))
    +      return s.round.toInt
    +    } else if (index == bins - 1) {
    +      m_b = getCounter(index) +
    +        (-getCounter(index)) * (b - getValue(index)) / (upper - getValue(index))
    +      s = (getCounter(index) + m_b) *
    +        (b - getValue(index)) / (2 * (upper - getValue(index)))
    +    } else {
    +      m_b = getCounter(index) + (getCounter(index + 1) - getCounter(index)) *
    +        (b - getValue(index)) / (getValue(index + 1) - getValue(index))
    +      s = (getCounter(index) + m_b) *
    +        (b - getValue(index)) / (2 * (getValue(index + 1) - getValue(index)))
    --- End diff --
    
    What do you mean with mapping it to the area of the trapezoid? In the end we don't want to obtain an area but a number of elements, right?


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