Dive into Probabilistic Programming

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

Transcript

1. Dive into 

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

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

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7. https://pycon.jp/2015/ja/schedule/presentation/38/
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   ‣ [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
   

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

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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”
    …
    

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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”
    …
    

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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”
    …
    

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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”
    …
    

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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”
    …
    

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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
    

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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
    

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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
    

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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
    

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

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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)
    

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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)
    

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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)
    

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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)
    

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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)
    

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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)
    

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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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    ‣ [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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    ‣ PROBABILISTIC-PROGRAMMING.org
    ‣ Why Probabilistic Programming Matters, Beau Cronin, March 2013, (Japanese translation)
    ‣ The State of Probabilistic Programming « Some Thoughts on a Mysterious Universe
    

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    ‣ Probabilistic Programming for Advancing Machine Learning (PPAML), Dr. Suresh Jagannathan
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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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    ‣ Probabilistic Models of Cognition
    ‣ Forest - A Repository for Generative Models
    

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41. probmods.org
    

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42. forestdb.org
    

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    ‣ The MIT Probabilistic Computing Project
    ‣ "An Overview of Probabilistic Programming" by Vikash K. Mansinghka - YouTube, Strange Loop 2015
    ‣ MIT Media Lab | Vikash Mansinghka on Probabilistic Programming for Augmented Intelligence, 2016
    

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    ‣ Picture: A Probabilistic Programming Language for Scene Perception (figure from this page)
    ‣ Short probabilistic programming machine-learning code replaces complex programs for computer-vision tasks | KurzweilAI
    ‣ Picture: A Probabilistic Programming Language for Scene Perception - TechTalks.tv, prezi slide
    

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    ‣ OpenPPL: A Proposal for Probabilistic Programming in Julia — OpenPPL 0.1.0 documentation
    ‣ JuliaStats/PGM.jl: A Julia framework for probabilistic graphical models.
    ‣ Probabilistic Programming in Julia - Google Groups
    

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    ‣ PROBABILISTIC-PROGRAMMING.org
    ‣ Resources – PPAML
    

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    ‣ Research articles on probabilistic programming: PROBABILISTIC-PROGRAMMING.org
    

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