贝叶斯网(例子预测产品销量)

package main.scala.chap05

import com.cra.figaro.language._
import com.cra.figaro.library.atomic.discrete.{Binomial, Poisson}
import com.cra.figaro.library.compound.If
import com.cra.figaro.algorithm.sampling.Importance

object ProductDistribution {


  // 社交网络
  class Network(popularity: Double) {

    // 目标客户社交网络中的平均人数
    val numNodes = Poisson(popularity)
  }

  class Model(targetPopularity: Double, productQuality: Double, affordability: Double) {

    /**
      *
      * @param numFriends
      * @param productQuality
      * @return
      */
    def generateLikes(numFriends: Int, productQuality: Double): Element[Int] = {

      /**
        *
        * @param friendsVisited 已经得到产品信息的人
        * @param totalLikes 受访者中喜欢产品的人数
        * @param unprocessedLikes 尚未模拟向其朋友推销的人中喜欢产品的人数
        * @return
        */
      def helper(friendsVisited: Int, totalLikes: Int, unprocessedLikes: Int): Element[Int] = {
        if (unprocessedLikes == 0) Constant(totalLikes)
        else {
          val unvisitedFraction = //#C
            1.0 - (friendsVisited.toDouble - 1)/ (numFriends - 1) //#C
          val newlyVisited = Binomial(2, unvisitedFraction)
          val newlyLikes = Binomial(newlyVisited, Constant(productQuality))
          Chain(newlyVisited, newlyLikes,
                (visited: Int, likes: Int) =>
                  helper(friendsVisited + visited, totalLikes + likes, unprocessedLikes + likes - 1))
        }
      }
      helper(1, 1, 1)
    }

    // 随机一个社交网络
    val targetSocialNetwork = new Network(targetPopularity)

    // 目标是否喜好产品，基于产品质量
    val targetLikes = Flip(productQuality)

    // 如果目标喜欢产品，计算朋友喜欢产品的数量。
    val numberFriendsLike =
      Chain(targetLikes, targetSocialNetwork.numNodes,
            (l: Boolean, n: Int) =>
              if (l) generateLikes(n, productQuality); else Constant(0))

    // 喜欢产品的人购买产品的概率定义， 二项分布
    // 社交网络中的人数，产品质量0~1
    val numberBuy = Binomial(numberFriendsLike, Constant(affordability))
  }

  def predict(targetPopularity: Double, productQuality: Double, affordability: Double): Double = {
    val model = new Model(targetPopularity, productQuality, affordability)
    val algorithm = Importance(1000, model.numberBuy)
    algorithm.start()

    // 推理期望
    val result = algorithm.expectation(model.numberBuy, (i: Int) => i.toDouble)
    algorithm.kill()
    result
  }


  /**
    * Figaro is used as a simulation language,
    * predicts what will happen in the future.
    *
    * 也可以反向推理
    * @param args
    */
  def main(args: Array[String]) {
    println("Popularity\tProduct quality\tAffordability\tPredicted number of buyers")
    println("100       \t0.5            \t0.5          \t" + predict(100, 0.5, 0.5))
    println("100       \t0.5            \t0.9          \t" + predict(100, 0.5, 0.9))
    println("100       \t0.9            \t0.5          \t" + predict(100, 0.9, 0.5))
    println("100       \t0.9            \t0.9          \t" + predict(100, 0.9, 0.9))
    println("10        \t0.5            \t0.5          \t" + predict(10, 0.5, 0.5))
    println("10        \t0.5            \t0.9          \t" + predict(10, 0.5, 0.9))
    println("10        \t0.9            \t0.5          \t" + predict(10, 0.9, 0.5))
    println("10        \t0.9            \t0.9          \t" + predict(10, 0.9, 0.9))
  }
}