Dive into Probabilistic Programming

C6b97a47d5406cfdef50a5c755751c16?s=47 Sorami Hisamoto
September 03, 2016
Programming
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360

Dive into Probabilistic Programming

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

C6b97a47d5406cfdef50a5c755751c16?s=128

Sorami Hisamoto

September 03, 2016
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Transcript

  1. Dive into 
 Probabilistic Programming  ֬཰తϓϩάϥϛϯάͲ͏Ͱ͠ΐ͏ !TPSBNJ +VMJB5PLZP 

  2. EJTDMBJNFS *`NKVTUBOPWJDFTMJEFTQSPCBCMZDPOUBJOFSSPST 1MFBTFEPIBWFBMPPLBUUIFSFGFSSFENBUFSJBMT

  3. 1SPCBCJMJTUJD1SPHSBNNJOH ֬཰తϓϩάϥϛϯά

  4. 1SPCBCJMJTUJD1SPHSBNNJOH ֬཰తϓϩάϥϛϯά

  5. https://pycon.jp/2015/ja/schedule/presentation/38/

  6. https://pycon.jp/2015/ja/schedule/presentation/38/

  7. https://pycon.jp/2015/ja/schedule/presentation/38/ ֬཰తʁ֬཰࿦తʁ

  8. 1SPHSBNNJOHlQSPCBCJMJTUJDEJTUSJCVUJPOTzʜ ✦ 1SPCBCJMJTUJD1SPHSBNT  4BNQMJOH
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 DPOEJUJPOWBMVFTPGWBSJBCMFTJOBQSPHSBNWJBPCTFSWBUJPO 5

    ‣ [Gordon+ 2014] "Probabilistic Programming", ICSE Future of Software Engineering ‣ What is probabilistic programming? - The PL Enthusiast ‣ The State of Probabilistic Programming « Some Thoughts on a Mysterious Universe

  9. &YBNQMFqJQQJOHDPJOT ✦ 4BZXFIBWFBDPJO XJUIVOLOPXOCFOEJOFTT ✦ 8FqJQJUBDPVQMFUJNFT ✦ 8FUIFOlHVFTTzJU`TCFOEJOFTT 6 ‣

    [Gordon+ 2014] "Probabilistic Programming", ICSE Future of Software Engineering ‣ What is probabilistic programming? - The PL Enthusiast ‣ “Probabilistic Models of Cognition” Chapter 3 : Conditioning

  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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    (BNFPVUDPNFDPOEJUJPO4LJMM 9 ‣ TrueSkill™ Ranking System - Microsoft Research (figure from this page) ‣ TrueSkill — trueskill 0.4.4 documentation ‣ [Gordon+ 2014] "Probabilistic Programming", ICSE Future of Software Engineering

  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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    ✦ 4BNQMJOH ✦ .$.$ ʜ 13 ‣ [Gordon+ 2014] "Probabilistic Programming", ICSE Future of Software Engineering ‣ The Design and Implementation of Probabilistic Programming Languages ‣ “Probabilistic Models of Cognition” Chapter 7. Algorithms for inference

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     l8JUI-FTT&YQFSUJTF&OBCMFYNPSFQSPHSBNNFSTz ✦ 4VNNFS4DIPPMT 16 ‣ Probabilistic Programming for Advancing Machine Learning (PPAML), Dr. Suresh Jagannathan ‣ PPAML Wiki ‣ PPAML Kickoff Overview Slides (pdf), November 2013

  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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  41. probmods.org

  42. forestdb.org

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  54. 0QFO11-
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