Upgrade to Pro — share decks privately, control downloads, hide ads and more …

ベイズ深層学習(6.3)

catla
March 27, 2020

 ベイズ深層学習(6.3)

ベイズ深層学習 6.3節 生成ネットワークの構造学習

catla

March 27, 2020
Tweet

More Decks by catla

Other Decks in Science

Transcript

  1. ϕΠζਂ૚ֶश

    ੜ੒ωοτϫʔΫͷߏ଄ֶश
    ܡɹঘً

    View full-size slide

  2. ຊ೔ͷ಺༰
    ‣ੜ੒ωοτϫʔΫͱߏ଄ֶश
    ‣Πϯυྉཧաఔ
    ‣ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ

    View full-size slide

  3. ੜ੒ωοτϫʔΫͷߏ଄ֶश

    View full-size slide

  4. Πϯυྉཧաఔ
    Πϯυྉཧաఔ
    ແݶͷ਺ྻΛ࣋ͭόΠφϦߦྻΛੜ੒͢Δ֬཰Ϟσϧɽ
    ʲഎܠʳ
    ɹਂ૚ֶशͷϞσϧʹ͓͍ͯɼੑೳͷྑ͍ωοτϫʔΫߏ଄ΛܾΊΔ͜ͱ͸೉͍͠ɽ
    ΠϯυྉཧաఔΛ࢖͏͜ͱͰɼσʔλ͔Β༗ޮάϥϑͷߏ଄ʢྡ઀ߦྻʣͷਪఆ͕
    Մೳɽ
    ɹ
    ɹωοτϫʔΫͷ෯΍ਂ͞΋ϕΠζਪ࿦ͷ࿮૊ΈͰಉֶ࣌श͕ՄೳͱͳΔɽ·ͨɼΠϯ
    υྉཧաఔΛԠ༻͢Δͱɼજࡏม਺ͷ࣍ݩ਺ͳͲ΋ࣗಈܾఆͰ͖Δɽ

    View full-size slide

  5. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ɹ·ͣɼ ͷόΠφϦߦྻ Λߟ͑ɼ ͱͳΔ৔߹ͷ ͷੜ੒աఔΛߏங͢
    Δɽ·ͨɼ֤ཁૉ ͸ϕϧψʔΠ෼෍ ͔Βੜ੒͞ΕΔͱ͢Δɽ͞Β
    ʹϋΠύʔύϥϝʔλ Λ༻͍ͯɼύϥϝʔλ ͕ϕʔλ෼෍
    ͔Βੜ੒͞Ε͍ͯΔͱͨ͠Βɼߦྻ ͷ෼෍͸࣍ͷεϥΠυͷΑ͏ʹॻ͚Δɽ
    N × H M H → ∞ M
    mn,h
    ∈ {0,1} Bern(πh
    )
    α > 0,β > 0 πh
    Beta(αβ/H, β)
    M


    p(πh
    ) = Beta(αβ/H, β)
    =
    Γ (
    αβ
    H
    + β)
    Γ (
    αβ
    H ) + Γ(β)
    π
    αβ
    H
    −1
    h
    (1 − πh
    )β−1
    p(mn,h
    |πh
    ) = Bern(πh
    )
    = πmn,h
    h
    (1 − πh
    )1−mn,h
    πh
    α β
    mn,h
    n = 1,2,…, N
    h = 1,2,…, H

    View full-size slide

  6. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ

    ͱ͢Δͱ ͱͳΓɼશͯͷόΠφϦߦྻͷੜ੒֬཰͕ʹͳͬͯ͠·
    ͏ɽ
    p(M) =
    H

    h=1

    p(πh
    )
    {
    N

    n=1
    p(mn,h
    |πh
    )
    }
    dπh
    =
    H

    h=1

    Γ (
    αβ
    H
    + β)
    Γ (
    αβ
    H ) + Γ(β)
    π
    αβ
    H
    −1
    h
    (1 − πh
    )β−1
    {
    N

    n=1
    πmn,h
    h
    (1 − πh
    )1−mn,h
    }
    dπh
    =
    H

    h=1
    Γ (
    αβ
    H
    + β)
    Γ (
    αβ
    H ) + Γ(β)

    πNh
    + αβ
    H
    −1
    h
    (1 − πh
    )N−Nh
    +β−1dπh
    ( ∵ Nh
    =
    N

    n=1
    mn,h
    )
    =
    H

    h=1
    Γ (
    αβ
    H
    + β)
    Γ (
    αβ
    H ) + Γ(β)
    Γ (Nh
    + αβ
    H ) Γ(N − Nh
    + β)
    Γ (
    αβ
    H
    + β + N)
    H → ∞ p(M) → 0
    ( ∵ Beta(x, y) =
    Γ(x)Γ(y)
    Γ(x + y)
    < 1 where x > 1,y > 1)

    View full-size slide

  7. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ɹੜ੒֬཰͕ʹͳΔ͜ͱΛ๷͙ͨΊʹɼ ͷྻΛฒͼସ͑Δʢlofʣ͜ͱͰಉ͡ʹͳΔ
    Α͏ͳߦྻͷಉ஋ྨΛ ͱ͓͘ɽ
    ྫɿ ͷͱ͖ɼ

    ɹ ʹରͯ͠ ͱͨ͠ͱ͖ͷ෼෍ͷܭࢉ͸จݙ<>ΑΓɼ࣍ͷεϥΠυͷΑ͏
    ʹॻ͚Δɽ
    M
    [M]
    M =
    (
    1 0 0
    0 1 0
    0 0 1
    )
    [M] ∈
    (
    1 0 0
    0 1 0
    0 0 1
    )
    ,
    (
    0 1 0
    1 0 0
    0 0 1
    )
    ,
    (
    0 0 1
    0 1 0
    1 0 0
    )
    ,
    (
    1 0 0
    0 0 1
    0 1 0
    )
    p([M]) H → ∞
    [1] “Infinite Latent Feature Models and the Indian Buffet Process”, 2018

    View full-size slide

  8. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ɹɹɹɹɹɹɹ
    ͨͩ͠ɼ ͸ ʹ͋ΔόΠφϦྻʢྻϕΫτϧ͕ಉ͡ͳΒ΋ಉ͡ʣͷݸ਺Ͱɼಉ
    ͡όΠφϦྻͷฒͼସ͑ʹΑΔॏෳΛΩϟϯηϧ͢ΔͨΊʹׂΔɽ·ͨɼ ͸
    ͱͳΔΑ͏ͳྻ ͷݸ਺ɽ ͸ ͷظ଴஋ɽɹɹɹɹɹɹɹ
    ɹ͜ͷ෼෍͸ ͷߦΛަ׵ͯ͠΋มΘΒͳ͍ͷͰɹަ׵ՄೳੑɹΛ࣋ͭɽ
    p([M]) = ∑
    M∈[M]
    p(M)
    =
    H!

    i≥1
    Hi
    !
    H

    h=1
    Γ (
    αβ
    H
    + β)
    Γ (
    αβ
    H ) + Γ(β)
    Γ (Nh
    + αβ
    H ) Γ(N − Nh
    + β)
    Γ (
    αβ
    H
    + β + N)

    (αβ)H+

    i≥1
    Hi
    !
    exp(− ¯
    H+
    )
    H+

    h=1
    Γ (Nh) Γ(N − Nh
    + β)
    Γ (β + N)
    Hi
    M i i
    i H+
    Nh
    > 0 h ¯
    H+
    = α
    N

    n=1
    β
    n + β − 1
    H+
    M

    View full-size slide

  9. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    M =

    View full-size slide

  10. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ͸ಉ͡
    i
    M =

    View full-size slide

  11. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    M =
    1 2 3 4 2 5 6
    i

    View full-size slide

  12. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ɹແݶྻΛ࣋ͭόΠφϦߦྻͷੜ੒͸ɼΠϯυྉཧաఔͷखଓ͖ʹΑͬͯɼ࣍ͷΑ͏ʹ
    ߦ͏͜ͱ͕Ͱ͖Δɽ
    ɹ࠷ॳʹྉཧళʹདྷͨ٬͸ɼҎԼͷϙΞιϯ෼෍ʹैͬͯྉཧΛͱΔɽ

    ɹO൪໨ʹདྷͨ٬͸ɼ֬཰ ʹै֤ͬͯྉཧ ΛͱΓɼ࠷ޙʹ
    ʹैͬͯ৽͍͠ྉཧΛͱΔɽ
    Poi(α) =
    αx
    x!
    e−α
    Nh
    n + β − 1
    h
    Poi (
    αβ
    n + β − 1)
    ΠϯυྉཧաఔʢIBPʣͷखଓ͖

    View full-size slide

  13. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ
    ɹੜ੒͞ΕΔόΠφϦߦྻ ͷಛੑ
    w٬ਓ͋ͨΓͷྉཧͷ਺͸ ʹै͏ɽ
    wͱΒΕΔྉཧͷ૯਺ͷظ଴஋͸
    w٬ʹऔΒΕΔྉཧͷछྨͷ߹ܭ͸
    w શһ͕ಉ͡ྉཧΛબͿ

    w ٬ಉ͕࢜ಉ͡ྉཧΛબ͹ͳ͘ͳΔ

    M ∈ {0,1}N×∞
    Poi(α)

    ¯
    H+
    = α
    N

    n=1
    β
    n + β − 1
    lim
    β→0
    ¯
    H+
    = α
    lim
    β→∞
    ¯
    H+
    = Nα

    View full-size slide

  14. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ





    O
    Poi(α)
    Poi (
    αβ
    2 + β − 1)
    Poi (
    αβ
    3 + β − 1)
    Poi (
    αβ
    4 + β − 1 )
    Poi (
    αβ
    5 + β − 1)
    Nh
    n + β − 1
    Nh
    n + β − 1
    Nh
    n + β − 1
    Nh
    n + β − 1
    ग़యɿ8JLJQFEJB
    ϙΞιϯ෼෍

    View full-size slide

  15. Πϯυྉཧաఔ
    ʲແݶߦྻͷੜ੒ʳ





    O
    Nh
    n + β − 1
    ͳͷͰɼ
    ֬཰ ͰʹͳΔɽ
    N2
    = 3
    3
    4 + β − 1
    h = 1 h = 2 h = 3

    View full-size slide

  16. Πϯυྉཧաఔ
    ʲΪϒεαϯϓϦϯάʳ
    ɹσʔλ Λແݶ࣍ݩͷજࡏม਺ ͱόΠφϦߦྻ ʹΑͬͯɼੜ੒ϞσϧΛϞσϧԽ
    ͢ΔͱҎԼͷΑ͏ʹͳΔɽ

    ɹ ͕ ͷΑ͏ʹղੳతʹੵ෼আڈͰ͖ΔͱԾఆͨ͠৔߹ɼ
    ΪϒεαϯϓϦϯάʹΑͬͯࣄޙ෼෍ ͔Β֤ Λ࣍ͷΑ͏ʹαϯϓϦϯάͰ
    ͖Δɽ

    ɹ ͔Β ͕αϯϓϦϯά͞ΕΔ֬཰͸ɼΠϯυྉཧաఔʹ͓͍ͯ
    ਓ͕ྉཧΛऔͬͨޙʹ࠷ޙͷ ൪໨ͷ٬͕ ൪໨ͷྉཧΛͱΔ͜ͱʹରԠ͍ͯ͠
    Δɽ
    X θ M
    p(X, M, θ) = p(X|M, θ)p(M)p(θ)
    θ p(X|M) =

    p(X|M, θ)p(θ)dθ
    p(M|X) mn,h
    p(mn,h
    = 1|M\(n,h)
    , X) ∝ p(X|M)p(mn,h
    = 1|M\(n,h)
    )
    p(mn,h
    |M\(n,h)
    ) mn,h
    = 1
    n − 1 n h

    View full-size slide

  17. Πϯυྉཧաఔ
    ʲΪϒεαϯϓϦϯάʳ
    ɹ͕ͨͬͯ͠ɼ ͱͳΔ͋Δ ݸ໨ͷ஋ ͸ɼΪϒεαϯϓϦϯά
    Λ༻͍ͯɼ֬཰ ͱ໬౓ Λܭࢉ͢Δ͜ͱʹΑΓαϯϓϦϯάͰ͖Δɽ
    ಉ༷ʹ ͱͳΔΑ͏ͳ৽نόΠφϦྻͷੜ੒͸ɼ৽نʹੜ੒͞ΕΔྻͷ਺
    ͷ֬཰͕ ͱ໬౓ ʹΑΓܭࢉͰ͖Δɽ৽نʹ௥Ճ͞ΕΔྻ਺͸Ճ
    ࢉແݶݸଘࡏ͢ΔͨΊɼݫີʹ͸ ΛແݶճධՁ͢Δඞཁ͕͋Δ͕ɼۙࣅͯ͠༗
    ݶͷީิ਺ͰܭࢉΛଧͪ੾Δํ๏͕࢖ΘΕΔɽʢྫɿ ͷΑ͏ʹଧͪ੾Δɽʣ
    N\n,h
    = ∑
    n′≠n
    mn′,h
    > 0 h mn,h
    N\n,h
    n + β − 1
    p(X|M)
    N\n,h
    = 0 Hnew
    Poi(
    αβ
    N + β − 1
    ) p(X|M)
    p(X|M)
    Hnew ≤ 10
    p(mn,h
    = 1|M\(n,h)
    , X) ∝ p(X|M)p(mn,h
    = 1|M\(n,h)
    )

    View full-size slide

  18. Πϯυྉཧաఔ
    ʲΪϒεαϯϓϦϯάʳ
    ɹ͕ͨͬͯ͠ɼ ͱͳΔ͋Δ ݸ໨ͷ஋ ͸ɼΪϒεαϯϓϦϯά
    Λ༻͍ͯɼ֬཰ ͱ໬౓ Λܭࢉ͢Δ͜ͱʹΑΓαϯϓϦϯάͰ͖Δɽ
    ಉ༷ʹ ͱͳΔΑ͏ͳ৽نόΠφϦྻͷੜ੒͸ɼ৽نʹੜ੒͞ΕΔྻͷ਺
    ͷ֬཰͕ ͱ໬౓ ʹΑΓܭࢉͰ͖Δɽ৽نʹ௥Ճ͞ΕΔྻ਺͸Ճ
    ࢉແݶݸଘࡏ͢ΔͨΊɼݫີʹ͸ ΛແݶճධՁ͢Δඞཁ͕͋Δ͕ɼۙࣅͯ͠༗
    ݶͷީิ਺ͰܭࢉΛଧͪ੾Δํ๏͕࢖ΘΕΔɽʢྫɿ ͷΑ͏ʹଧͪ੾Δɽʣ
    N\n,h
    = ∑
    n′≠n
    mn′,h
    > 0 h mn,h
    N\n,h
    n + β − 1
    p(X|M)
    N\n,h
    = 0 Hnew
    Poi(
    αβ
    N + β − 1
    ) p(X|M)
    p(X|M)
    Hnew ≤ 10
    p(mn,h
    = 1|M\(n,h)
    , X) ∝ p(X|M)p(mn,h
    = 1|M\(n,h)
    )

    View full-size slide

  19. Πϯυྉཧաఔ
    ʲΪϒεαϯϓϦϯάʳ
    ɹ͕ͨͬͯ͠ɼ ͱͳΔ͋Δ ݸ໨ͷ஋ ͸ɼΪϒεαϯϓϦϯά
    Λ༻͍ͯɼ֬཰ ͱ໬౓ Λܭࢉ͢Δ͜ͱʹΑΓαϯϓϦϯάͰ͖Δɽ
    ಉ༷ʹ ͱͳΔΑ͏ͳ৽نόΠφϦྻͷੜ੒͸ɼ৽نʹੜ੒͞ΕΔྻͷ਺
    ͷ֬཰͕ ͱ໬౓ ʹΑΓܭࢉͰ͖Δɽ৽نʹ௥Ճ͞ΕΔྻ਺͸Ճ
    ࢉແݶݸଘࡏ͢ΔͨΊɼݫີʹ͸ ΛແݶճධՁ͢Δඞཁ͕͋Δ͕ɼۙࣅͯ͠༗
    ݶͷީิ਺ͰܭࢉΛଧͪ੾Δํ๏͕࢖ΘΕΔɽʢྫɿ ͷΑ͏ʹଧͪ੾Δɽʣ
    N\n,h
    = ∑
    n′≠n
    mn′,h
    > 0 h mn,h
    N\n,h
    n + β − 1
    p(X|M)
    N\n,h
    = 0 Hnew
    Poi(
    αβ
    N + β − 1
    ) p(X|M)
    p(X|M)
    Hnew ≤ 10
    ൪໨ʹདྷͨ٬͕ ൪໨
    ͷྉཧΛऔΔ֬཰
    n h
    ൪໨ʹདྷͨ٬͕৽͍͠
    ྉཧΛऔΔ֬཰
    n
    p(mn,h
    = 1|M\(n,h)
    , X) ∝ p(X|M)p(mn,h
    = 1|M\(n,h)
    )

    View full-size slide

  20. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ɹจݙ<>ʹج͖ͮɼඇઢܗΨ΢ε৴೦ωοτϫʔΫʢOPOMJOFBS(BVTTJBOCFMJFG
    OFUXPSLʣͱ͍͏ੜ੒ϞσϧΛ࢖ͬͯ%//Λߏ੒͢Δɽ
    ʲඇઢܗΨ΢ε৴೦ωοτϫʔΫʳ
    ɹ ૚ͷωοτϫʔΫΛߟ͑Δɽ
    ɹ ɿ૚໨ͷϢχοτ਺ɽ
    ɹ ɿ૚໨ͷ ൪໨ͷϢχοτɽ
    ɹ ɿ
    ྡ઀ߦྻʢʹશ݁߹૚ʹର͢ΔϚεΫʣɽཁૉ ͸ɼ ͔Β ʹ໼ҹ͕ଘࡏ͢Δ͜ͱ
    Λҙຯ͢Δɽ
    ɹ ɿ૚໨ͷॏΈύϥϝʔλɽ
    ɹ ɿ૚໨ͷόΠΞεύϥϝʔλɽ
    ɹ ɿ૚໨ͷ׆ੑɽ
    ͱ͓͘ɽ
    L
    Hl
    l
    z(l)
    h
    l h
    M(l) ∈ ℝHl−1
    ×Hl
    m(l)
    h,h′
    = 1 z(l)
    h′
    z(l−1)
    h
    W(l) ∈ ℝHl−1
    ×Hl l
    b ∈ ℝHl l
    a(l) l
    [2] “Learning the Structure of Deep Sparse Graphical Models”, 2010

    View full-size slide

  21. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲඇઢܗΨ΢ε৴೦ωοτϫʔΫʳ
    ɹ׆ੑ͸ҎԼͷΑ͏ʹॻ͚Δɽ

    ͞Βʹ׆ੑ ʹ͸Ψ΢ε෼෍͔ΒͷϊΠζ͕ՃΘΔͱ͢Δɽ

    ӅΕϢχοτ ͸ҎԼͷΑ͏ʹม׵͞Ε͍ͯΔͱ͢Δɽ

    a(l) = (W(l+1) ⊙ M(l+1))z(l+1) + b(l)
    a(l)
    h
    ˜
    a(l)
    h
    = a(l)
    h
    + ϵ
    ϵ ∼ (0,ν(l)
    h
    )
    z(l)
    h
    z(l)
    h
    = ϕ( ˜
    a(l)
    h
    )
    ϕ( ⋅ ) = Tanh( ⋅ )

    View full-size slide

  22. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲඇઢܗΨ΢ε৴೦ωοτϫʔΫʳ
    ɹ͢Δͱɼ ͷ෼෍͸ҎԼͷΑ͏ʹٻΊΒΕΔɽʢ֬཰ม਺ͷม਺ม׵ʣ


    ɹ·ͨɼ ͱ ͸Ψ΢εࣄલ෼෍ɼ ʹ͸ΨϯϚࣄલ෼෍Λ༩͑Δɽʢڞ໾ࣄલ
    ෼෍ʣ
    w ͕খ͍͞ɹˠ஋ͷۃ୺ͳ஋ΛͱΔɽ
    w ͕େ͖͍ɹˠ΄΅ܾఆతͳ஋ΛͱΔɽ
    ͞Βʹɼ ͱ͢Δɽ
    z(l)
    h
    p(z(l)
    h
    |a(l)
    h
    , ν(l)
    h
    ) = (ϕ−1(z(l)
    h
    )|a(l)
    h
    , ν(l)
    h
    )
    ∂ ˜
    a(l)
    h
    ∂z(l)
    h
    =
    N(ϕ−1(z(l)
    h
    )|a(l)
    h
    , ν(l)
    h
    )
    ϕ′(ϕ−1(z(l)
    h
    ))
    ϕ′(a) =
    d
    da
    ϕ(a)
    W(l)
    h
    b(l) ν(l)
    h
    ν(l)
    h
    ν(l)
    h
    z(0)
    h
    = xh
    ∈ (−1,1)

    View full-size slide

  23. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲඇઢܗΨ΢ε৴೦ωοτϫʔΫʳ
    ɹϞσϧશମͷಉ࣌෼෍͸ҎԼͷΑ͏ʹॻ͚Δ

    p(X, Z, M, W, b, ν)
    = p(W)p(b)p(ν)p(M)
    N

    n=1
    p(xn
    |zn
    , M, W, b, ν)p(zn
    |M, W, b, ν)

    View full-size slide

  24. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲ௚ྻΠϯυྉཧաఔʳ
    ɹ͖ͬ͞ͷಉ࣌෼෍ʹؔͯ͠ɼ૚਺΍ӅΕϢχοτ਺ʹࣗ༝౓Λ࣋ͨͤΔΑ͏ʹ֦ு͢
    Δɽ
    ɹ·ͣɼ Λߟ͑Δɽߦ਺͸ ͷ࣍ݩ਺ ͰݻఆͳͷͰɼΠϯυྉཧաఔͷ٬਺ͱΈ
    ͳ͢ɽ࣍ʹ Λߟ͑Δͱɼߦ਺͸ΠϯυྉཧաఔʹΑͬͯಘΒΕͨ ͷྻ਺ ʹ
    ݻఆ͢Δඞཁ͕͋Γɼ͜Ε΋ΠϯυྉཧաఔͰαϯϓϦϯάͰ͖Δɽ͜ΕΛ܁Γฦ࣮͠
    ߦͯ͠ɼ ɼ ɼ ɼ ͷΑ͏ʹαϯϓϦϯά͢Δ͜ͱͰωοτϫʔΫΛߏஙͰ
    ͖Δɽ
    M(1) x H0
    M(2) M(1) H1
    M(1) M(2) M(3) …

    x ∈ ℝH0
    M(1) ∈ ℝH0
    ×H1
    M(2) ∈ ℝH1
    ×H2
    M(3) ∈ ℝH2
    ×H3
    IBP IBP IBP IBP

    View full-size slide

  25. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲ௚ྻΠϯυྉཧաఔʳ
    ɹɹ݁Ռతʹɼ૚਺΍ӅΕϢχοτ਺ʹ্ݶ͕ͳ͘ͳΔɽ͜ͷΑ͏ʹͳແݶͷྻ਺Λ࣋
    ͭόΠφϦߦྻͷ࿈࠯Λੜ੒͍ͯ͘͠աఔΛɹ௚ྻΠϯυྉཧաఔɹͱݺͿɽ
    ɹ
    ɹग़ྗ૚΋ݻఆ͡Όͳ͍ʁͱࢥ͚ͬͨͲɼඞͣ༗ݶͷਂ͞Ͱఀࢭ͢Δ͜ͱ͕ࣔ͞ΕΔΒ
    ͍͠<>ɽ
    ɹ
    ɹਤΛݟͯ΋Β͑Ε͹૝૾͖ͭ΍͍͢ɽ

    View full-size slide

  26. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲ௚ྻΠϯυྉཧաఔʳ
    2ɽͲͷΑ͏ʹಉ࣌෼෍Λਪ࿦͢Δ͔ɽ
    "ɹ.$.$Ͱۙࣅతʹਪ࿦Ͱ͖Δɽ
    ʢ۩ମྫʣӅΕϢχοτͷू߹ ɼόΠφϦߦྻͷू߹ ɼύϥϝʔλͷू߹
    ͷͭͷϒϩοΫʹ෼͚ͯɼΪϒεαϯϓϦϯάʹجͮ͘ަޓαϯϓϦϯάΛߦ͑Δɽ
    Z M {W, b, ν}
    Z ∼ p(Z|X, M, W, b, ν)
    M ∼ p(M|X, Z, W, b, ν) W, b, ν ∼ p(W, b, ν|X, Z, M)
    zn
    ∼ p(zn
    |xn
    , M, W, b, ν)
    mn,h
    ∼ p(mn,h
    |X, Z, W, b, ν, M\(n,h)
    ) W ∼ p(W|X, Z, M, b, ν) b ∼ p(W, b, ν|X, Z, M, W, ν)
    ν ∼ p(W, b, ν|X, Z, M, W, b)

    View full-size slide

  27. ແݶͷχϡʔϥϧωοτϫʔΫϞσϧ
    ʲ௚ྻΠϯυྉཧաఔʳ
    ɹ ͷαϯϓϧ͕༩͑ΒΕ͍ͯΔঢ়گͰ͸ɼωοτϫʔΫ͕ݻఆ͞Ε͍ͯΔͷͰɼҎલ
    ΍ͬͨΑ͏ͳ௨ৗͷੜ੒ωοτϫʔΫͷਪ࿦໰୊ʹؼணɽ
    ɹ ͷαϯϓϧ͕༩͑ΒΕ͍ͯΔঢ়گͰ͸ɼ ͷࣄલ෼෍͸ڞ໾ࣄલ෼෍͔Βબ
    ୒͍ͯ͠ΔͷͰɼ ͷαϯϓϦϯά͸༰қʹՄೳɽ
    ɹҰํͰɼ ΍ ͷαϯϓϦϯά͸ෳࡶɽϝτϩϙϦεɾϔΠεςΟϯάε๏Λ࢖͏͜
    ͱͰ࣮ࢪͰ͖Δɽ
    M
    Z {W, b, ν}
    {W, b, ν}
    Z M

    View full-size slide