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Dive into Probabilistic Programming

Sorami Hisamoto
September 03, 2016
Programming
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560

Dive into Probabilistic Programming

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

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
 ESBXWBMVFTBUSBOEPNGSPNEJTUSJCVUJPOT  $POEJUJPOJOH
 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

  20. &YBNQMFSBUJOHUIFPOMJOFHBNFQMBZFST ✦ 1MBZFSTIBWFl 5SVF 4LJMMzBOEl1FSGPSNBODFz ✦ 1FSGPSNBODFJTCBTFEPO4LJMMT 
 BOEJUWBSJFTGSPNHBNFUPHBNF ✦

    (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)

  28. 4JNJMBSFYBNQMF
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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

  31. -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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 TDJLJUMFBSOJTDPPM CVUZPVDBO`UDPOTUSVDUOPWFMNPEFMTXJUIJUEJGGFSFOUVTFDBTFT 15 ‣ 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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     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

  35. "OEUIFSF`SFTPNBOZ MBOHVBHFTTZTUFNTʜ

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    4UBUB +VMJB 20 ‣ Stan, official website (logo from this page) ‣ Bob Carpenter: Stan.jl - Statistical Modeling and Inference Made Easy - YouTube, JuliaCon 2015 ‣ Stan is Turing Complete. So what? - Statistical Modeling, Causal Inference, and Social Science

  38. 1Z.$ ✦ 1ZUIPO ✦ 1Z.$ 1Z.$ ✦ l#BZFTJBO.FUIPETGPS)BDLFSTz 21 ‣

    pymc-devs/pymc: PyMC: Bayesian Stochastic Modelling in Python ‣ Probabilistic Programming & Bayesian Methods for Hackers (figure from this page) ‣ (ja) “ؠ೾σʔλαΠΤϯε Vol.1” [ಛू] ϕΠζਪ࿦ͱMCMCͷϑϦʔιϑτ

  39. KB ؠ೾σʔλαΠΤϯε7PM <ಛू>ϕΠζਪ࿦ͱ.$.$ͷϑϦʔιϑτ Image from sites.google.com/site/iwanamidatascience/

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  41. probmods.org

  42. forestdb.org

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  45. *OGFS/&5'VO5BCVMBS ✦ .JDSPTPGU3TFBSDI ✦ *OGFS/&5'VO ✦ 'QSPCBCJMJTUJDNPEFMJOHMBOHVBHF ✦ 5BCVMBSTDIFNBESJWFOBQQSPBDI ✦

    BWBJMBCMFBTBO&YDFMBEEJO 28 ‣ ETAPS 2016 - Structure and Interpretation of Probabilistic Programs - Andrew D. Gordon - YouTube ‣ Infer.NET Fun - Microsoft Research ‣ [Gordon+ 2014] "Probabilistic Programming", ICSE Future of Software Engineering (figure from this paper)

  46. 'JHBSP ✦ 4DBMBCBTFE0CKFDU0SJFOUFE ✦ 5IFSF`TBCPPL  29 ‣ Avi Pfeffer

    “Practical Probabilistic Programming” (Manning, 2016) (figure from this page) ‣ Probabilistic Programming Language | Probabilistic Modeling ‣ Avi Pfeffer - Practical Probabilistic Programming with Figaro - MLconf SEA 2016 - YouTube, slide

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  48. +VMJB

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  50. .$.$ ✦ +VMJB4UBUT.$.$KMDVSSFOUMZBQMBDFIPMEFSSFQPTJUPSZ ✦ +VMJB4UBUT-PSBKM ✦ CSJBOKTNJUI.BNCBKM ✦ HPFENBO4UBOKM ✦

    HPFENBO+BHTKM ✦ PMPGTFO+"(4KM ✦ -BVSFODF"TEpPVTEGKM QSFWJPVTMZLOPXOBT5VSJOHKM 33 ‣ scidom (Theodore Papamarkou) (figure from this page), Lora User Guide — Lora 0.5.3 documentation ‣ Names of Existing MCMC Packages · Issue #1 · JuliaStats/MCMC.jl ‣ JuliaTokyo #2 ͰϞϯςΧϧϩ๏ʹ͍ͭͯ࿩͖ͯ͠·ͨ͠ - ΓΜ͕͝Ͱ͍ͯΔ

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    ✦ l1SPCBCJMJTUJD1SPHSBNT8IJDI.BLF $PNNPO 4FOTFzCZ;FOOB5BWBSFT :PV5VCF 34 ‣ https://github.com/zenna/Sigma.jl ‣ Sigma.jl’s documentation — Sigma 0.0.1 documentation ‣ "Probabilistic Programs Which Make (Common) Sense" by Zenna Tavares - YouTube, Strange Loop 2015

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  54. 0QFO11-
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  55. 8IFSFUPTUBSU

  56. 8IFSFUPTUBSU ✦ 3FBEJOHT ✦ 8IBUJTQSPCBCJMJTUJDQSPHSBNNJOH 5IF1-&OUIVTJBTU ✦ 5IF4UBUFPG1SPCBCJMJTUJD1SPHSBNNJOHm4PNF5IPVHIUTPOB.ZTUFSJPVT6OJWFSTF ✦ *OUFSBDUJWF5VUPSJBMT

    ✦ 1SPCBCJMJTUJD.PEFMTPG$PHOJUJPO $IVSDI  ✦ 5IF%FTJHOBOE*NQMFNFOUBUJPOPG1SPCBCJMJTUJD1SPHSBNNJOH-BOHVBHFT 8FC11- 39 ‣ PROBABILISTIC-PROGRAMMING.org ‣ Resources – PPAML

  57. 4PNFQBQFST ✦ <(PSEPO >1SPCBCJMJTUJD1SPHSBNNJOHz
 *$4&'VUVSFPG4PGUXBSF&OHJOFFSJOH ✦ <(PPENBO >l$IVSDIBMBOHVBHFGPSHFOFSBUJWFNPEFMTz
 6ODFSUBJOUZJO"SUJpDJBM*OUFMMJHFODF 6"*

     ✦ 1I%5IFTFT ✦ "OESFBT4UVIMNÛMMFS l.PEFMJOH$PHOJUJPOXJUI1SPCBCJMJTUJD1SPHSBNT3FQSFTFOUBUJPOTBOE"MHPSJUINTz ✦ %BOJFM.3PZ l$PNQVUBCJMJUZ JOGFSFODFBOENPEFMJOHJOQSPCBCJMJTUJDQSPHSBNNJOHz ✦ 7JLBTI.BOTJOHILB l/BUJWFMZ1SPCBCJMJTUJD$PNQVUBUJPOz 40 ‣ Research articles on probabilistic programming: PROBABILISTIC-PROGRAMMING.org