Bayesian model:

• P(c|x,n) = p(x,n|c)P(c) / p(x,n)
• P(x|n,c) = P(x,n|c) / P(n|c) implies P(x,n|c) = P(x|n,c) * P(n|c)
• so P(c|x,n) = p(x,n|c)P(c) / p(x,n) = P(x|n,c) * P(n|c) * P(c) / p(x,n) ~ P(x|n,c) * P(n|c) * P(c)

distribution:

• P(c) ~ MN(n=1, p1,p2,...,p5)
• P(n|c) ~ Poi(l) (the count of engagement data - 1 for each label point, -1 is to make fit the support of poisson distribution)
• P(x|n,c) = P(positions|n,c) * P(clicks|n,c) * P(views|n,c) where
  • positions|n,c ~ MN(n, p1, p2,...,pa),
  • clicks|n,c ~ MN(n, p1, p2,...,pb),
  • views|n,c ~ MN(n, p1, p2,...,pc), and
  • a, b, c are contants that is pre-defined by high density regions(HDR) or modeler

dotation:

• Poi: Poisson
• MN: Multinomial
• p1, p2,... : constant probabilities using HDR or deterministic binnings

to run:

• sbt clean; sbt assembly; scala -J-Xmx1024m -cp target/scala-2.11/bayesian-assembly-0.0.1.jar model.Driver
• output is new_label.txt