Dive into Probabilistic Programming

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Dive into   Probabilistic Programming ֬཰తϓϩάϥϛϯάͲ͏Ͱ͠ΐ͏ !TPSBNJ +VMJB5PLZP

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1SPCBCJMJTUJD1SPHSBNNJOH ֬཰తϓϩάϥϛϯά

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1SPCBCJMJTUJD1SPHSBNNJOH ֬཰తϓϩάϥϛϯά

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

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

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

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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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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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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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### 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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-BUFOU%JSJDIMFU"MMPDBUJPOJOWBSJPVTGPSNT 14 ‣ [Tang+ 2014] Understanding the Limiting Factors of Topic Modelling via Posterior Contraction Analysis // Speaker Deck ‣ example-models/lda.stan at master · stan-dev/example-models ‣ Latent Dirichlet Allocation - Forest

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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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probmods.org

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forestdb.org

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#BZFT%#7FOUVSF ✦ 5IF.*51SPCBCJMJTUJD$PNQVUJOH1SPKFDU ✦ #BZFT%# ✦ #2- #BZFTJBO2VFSZ-BOVBHF FYUFOTJPOPG42-&45*."5& 4*.6-"5& ʜ ✦ 7FOUVSF ✦ QSPCBCJMJTUJDDPNQVUJOHQMBUGPSN  )PTUTBQQMJDBUJPOTMJLF#BZFT%#1SPHSBNNFEQSJNBSJMZJOl7FOUVSF4DSJQUz 27 ‣ 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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+VMJB

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0QFO11-  "1SPQPTBMGPS1SPCBCJMJTUJD1SPHSBNNJOHJO+VMJB 37 ‣ 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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