Dive into Probabilistic Programming

http://juliatokyo.connpass.com/event/36710/

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 Probabilistic Programming
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10. makeCoin(0.9) #“head”with probability 0.9 makeCoin(0.1) #“tail”with probability 0.9 coin = makeCoin(0.5) # distribution flip(coin) # sampling => “head” flip(coin) => “head” flip(coin) => “tail” …
11. makeCoin(0.9) #“head”with probability 0.9 makeCoin(0.1) #“tail”with probability 0.9 coin = makeCoin(0.5) # distribution flip(coin) # sampling => “head” flip(coin) => “head” flip(coin) => “tail” …
12. makeCoin(0.9) #“head”with probability 0.9 makeCoin(0.1) #“tail”with probability 0.9 coin = makeCoin(0.5) # distribution flip(coin) # sampling => “head” flip(coin) => “head” flip(coin) => “tail” …
13. makeCoin(0.9) #“head”with probability 0.9 makeCoin(0.1) #“tail”with probability 0.9 coin = makeCoin(0.5) # distribution flip(coin) # sampling => “head” flip(coin) => “head” flip(coin) => “tail” …
14. makeCoin(0.9) #“head”with probability 0.9 makeCoin(0.1) #“tail”with probability 0.9 coin = makeCoin(0.5) # distribution flip(coin) # sampling => “head” flip(coin) => “head” flip(coin) => “tail” …
15. coin2 = makeCoin(param) # a coin with unknown parameter result1 = flip(coin2) observe(result1 == head) # conditioning result2 = flip(coin2) observe(result2 == head) result3 = flip(coin2) observe(result3 == head) infer(param) # => probably higher than 0.5
16. coin2 = makeCoin(param) # a coin with unknown parameter result1 = flip(coin2) observe(result1 == head) # conditioning result2 = flip(coin2) observe(result2 == head) result3 = flip(coin2) observe(result3 == head) infer(param) # => probably higher than 0.5
17. coin2 = makeCoin(param) # a coin with unknown parameter result1 = flip(coin2) observe(result1 == head) # conditioning result2 = flip(coin2) observe(result2 == head) result3 = flip(coin2) observe(result3 == head) infer(param) # => probably higher than 0.5
18. coin2 = makeCoin(param) # a coin with unknown parameter result1 = flip(coin2) observe(result1 == head) # conditioning result2 = flip(coin2) observe(result2 == head) result3 = flip(coin2) observe(result3 == head) infer(param) # => probably higher than 0.5
19. coin2 = makeCoin(param) # a coin with unknown parameter result1 = flip(coin2) observe(result1 == head) # conditioning result2 = flip(coin2) observe(result2 == head) result3 = flip(coin2) observe(result3 == head) infer(param) # => probably higher than 0.5
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21. skillA = Normal(μ=100, σ=10) skillB = Normal(μ=100, σ=10) skillC = Normal(μ=100, σ=10) ### 1st game : A vs B # players have probabilistic performance perfA1 = Normal(skillA, 15) perfB1 = Normal(skillB, 15) # A won => condition the skills observe(perfA1 > perfB1)
22. skillA = Normal(μ=100, σ=10) skillB = Normal(μ=100, σ=10) skillC = Normal(μ=100, σ=10) ### 1st game : A vs B # players have probabilistic performance perfA1 = Normal(skillA, 15) perfB1 = Normal(skillB, 15) # A won => condition the skills observe(perfA1 > perfB1)
23. skillA = Normal(μ=100, σ=10) skillB = Normal(μ=100, σ=10) skillC = Normal(μ=100, σ=10) ### 1st game : A vs B # players have probabilistic performance perfA1 = Normal(skillA, 15) perfB1 = Normal(skillB, 15) # A won => condition the skills observe(perfA1 > perfB1)
24. skillA = Normal(μ=100, σ=10) skillB = Normal(μ=100, σ=10) skillC = Normal(μ=100, σ=10) ### 1st game : A vs B # players have probabilistic performance perfA1 = Normal(skillA, 15) perfB1 = Normal(skillB, 15) # A won => condition the skills observe(perfA1 > perfB1)
25. ### 2nd game : B vs C perfB2 = Normal(skillB, 15) perfC2 = Normal(skillC, 15) observe(perfB2 > perfC2) ### 3rd game : A vs C perfA3 = Normal(skillA, 15) perfC3 = Normal(skillC, 15) observe(perfA3 > perfC3) infer(skillA) # => Normal(μ=105.7, σ=0.11) infer(skillB) # => Normal(μ=100.0, σ=0.11) infer(skillC) # => Normal(μ=94.3, σ=0.11)
26. ### 2nd game : B vs C perfB2 = Normal(skillB, 15) perfC2 = Normal(skillC, 15) observe(perfB2 > perfC2) ### 3rd game : A vs C perfA3 = Normal(skillA, 15) perfC3 = Normal(skillC, 15) observe(perfA3 > perfC3) infer(skillA) # => Normal(μ=105.7, σ=0.11) infer(skillB) # => Normal(μ=100.0, σ=0.11) infer(skillC) # => Normal(μ=94.3, σ=0.11)
27. ### 2nd game : B vs C perfB2 = Normal(skillB, 15) perfC2 = Normal(skillC, 15) observe(perfB2 > perfC2) ### 3rd game : A vs C perfA3 = Normal(skillA, 15) perfC3 = Normal(skillC, 15) observe(perfA3 > perfC3) infer(skillA) # => Normal(μ=105.7, σ=0.11) infer(skillB) # => Normal(μ=100.0, σ=0.11) infer(skillC) # => Normal(μ=94.3, σ=0.11)
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34. 14 • Application • Code Libraries • Programming Language • Compiler • Hardware The Probabilistic Programming Revolution • Model • Model Libraries • Probabilistic Programming Language • Inference Engine • Hardware Traditional Programming Probabilistic Programming Code models capture how the data was generated using random variables to represent uncertainty Libraries contain common model components: Markov chains, deep belief networks, etc. PPL provides probabilistic primitives & traditional PL constructs so users can express model, queries, and data Inference engine analyzes probabilistic program and chooses appropriate solver(s) for available hardware Hardware can include multi-core, GPU, cloud-based resources, GraphLab, UPSIDE/Analog Logic results, etc. High-level programming languages facilitate building complex systems Probabilistic programming languages facilitate building rich ML applications Approved for Public Release; Distribution Unlimited From PPAML Kickoff Overview Slides (pdf), November 2013
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