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ϕΠζͰ୯ճؼϞσϧΛߟ͑Δ
5IJNCMFF
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ઃఆ
܇࿅σʔλͷઆ໌ม ͱతม ͔ΒҎԼͷ
༧ଌΛٻΊΔ
ҎԼͷ୯ճؼϞσϧΛ༻͢Δ
x = (x1
, x2
, ⋯, xN
)T t = (t1
, t2
, ⋯, tN
)T
p(t*
|x*
, t, x)
p(t*
|x*
, w, β) =
𝒩
(t*
|w0
+ w1
x*
, β−1)
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۩ମతʹ
͜͏͍͏σʔλʹର͍͍ͯ͠ײ͡ʹύϥϝʔλ Λௐͯ͠ɺઢ
ΛҾ͖͍ͨɻ͜ͷσʔλେମ ͱͳ͍ͬͯΔɻ
w = (w0
, w1
)T
y = w0
+ w1
x t = − 2 + 2x
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ϕΠζͷఆཧ
p(A|B) =
p(A)p(B|A)
p(B)
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ࣄޙ QPTUFSJPS
ύϥϝʔλɺ σʔλ
ࣄޙΛ༻͍ͨύϥϝʔλͷਪఆ͕ϕΠζਪఆͰ͢ɻ
w t
p(w|t) =
p(w)p(t|w)
p(t)
∝ p(w)p(t|w)
(posterior) ∝ (prior)(likelihood)
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ࣄલ QSJPS
p(w) =
𝒩
(w|0, α−1I), α = 0.25
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ؔ MJLFMJIPPE
L(w) = p(t|w)
=
𝒩
(t|m, β−1I)
where m = (w0
+ w1
x1
, w0
+ w1
x2
, ⋯, w0
+ w1
xN
)T, β = 2.0
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ؔͷྫ
͜ͷΑ͏ͳ͍͍ײ͡ͷઢͩͱͱ͍͏େ͖͍ΛͱΔ
L((−2.1,2.2)T) = 0.39
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ؔͷྫ
͜ͷΑ͏ͳઢͩͱͱ͍͏ΛͱΔ
L((−1.0,0.0)T) = 0.29
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ؔͷྫ
͜ͷΑ͏ͳѱ͍ઢͩͱͱ͍͏খ͍͞ΛͱΔ
L((1.0, − 3.0)T) = 0.18
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ࣄલͱؔʢ࠶ܝʣ
ؔ MJLFMJIPPE
ࣄલ QSJPS
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ࣄલͱؔͷੵ
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ٻΊΒΕͨઢ
ࣄޙ ͷ࣌ʹ࠷େʹͳΔ
w = (−1.08,0.38)
L((−1.08,0.38)T) = 0.31
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͚ؔͩʢ࠷ਪఆʣͰ͍͍ͷͰ
ϕΠζʢࣄޙʣͩͱσʔλΛ͏·͘දݱͰ͖͍ͯͳ͍
࣮ࡍɺ͜ͷσʔλΛ୯ճؼϞσϧͰֶश͢ΔࡍʹϕΠζඞཁͳ͍
ʢ୯ճؼϞσϧ͕ཧղ͍͔͢͠Β༻͍ͨʣ
͔͠͠ɺҰൠʹϕΠζͰߟ͑ΔϝϦοτ͕ଟ͍
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ϕΠζͷಛ
w ύϥϝʔλʢ୯ճؼϞσϧͳΒ ʣʹ͍ͭͯ֬Λߟ͑ΒΕΔ
w ࣄલʹʢσʔλҎ֎ͷʣطͷใΛөͤ͞ΒΕΔ
w ֬ͷஞ࣍ߋ৽͕Ͱ͖Δ
w աֶशΛ͛Δʢਖ਼ଇԽʣ
w ʢଞʹ৭ʑ͋Δͱࢥ͍·͢ʣ
w
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͝ਗ਼ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠
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