ϕΠζͰ୯ճؼϞσϧΛߟ͑Δ5IJNCMFF1
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ઃఆ܇࿅σʔλͷઆ໌ม ͱతม ͔ΒҎԼͷ༧ଌΛٻΊΔҎԼͷ୯ճؼϞσϧΛ༻͢Δx = (x1, x2, ⋯, xN)T t = (t1, t2, ⋯, tN)Tp(t*|x*, t, x)p(t*|x*, w, β) =𝒩(t*|w0+ w1x*, β−1)2
۩ମతʹ͜͏͍͏σʔλʹର͍͍ͯ͠ײ͡ʹύϥϝʔλ Λௐͯ͠ɺઢΛҾ͖͍ͨɻ͜ͷσʔλେମ ͱͳ͍ͬͯΔɻw = (w0, w1)Ty = w0+ w1x t = − 2 + 2x3
ϕΠζͷఆཧp(A|B) =p(A)p(B|A)p(B)4
ࣄޙ QPTUFSJPSύϥϝʔλɺ σʔλࣄޙΛ༻͍ͨύϥϝʔλͷਪఆ͕ϕΠζਪఆͰ͢ɻw tp(w|t) =p(w)p(t|w)p(t)∝ p(w)p(t|w)(posterior) ∝ (prior)(likelihood)5
ࣄલ QSJPSp(w) =𝒩(w|0, α−1I), α = 0.256
ؔ MJLFMJIPPEL(w) = p(t|w)=𝒩(t|m, β−1I)where m = (w0+ w1x1, w0+ w1x2, ⋯, w0+ w1xN)T, β = 2.07
ؔͷྫ͜ͷΑ͏ͳ͍͍ײ͡ͷઢͩͱͱ͍͏େ͖͍ΛͱΔL((−2.1,2.2)T) = 0.398
ؔͷྫ͜ͷΑ͏ͳઢͩͱͱ͍͏ΛͱΔL((−1.0,0.0)T) = 0.299
ؔͷྫ͜ͷΑ͏ͳѱ͍ઢͩͱͱ͍͏খ͍͞ΛͱΔL((1.0, − 3.0)T) = 0.1810
ࣄલͱؔʢ࠶ܝʣؔ MJLFMJIPPEࣄલ QSJPS11
ࣄલͱؔͷੵ12
ٻΊΒΕͨઢࣄޙ ͷ࣌ʹ࠷େʹͳΔw = (−1.08,0.38)L((−1.08,0.38)T) = 0.3113
͚ؔͩʢ࠷ਪఆʣͰ͍͍ͷͰϕΠζʢࣄޙʣͩͱσʔλΛ͏·͘දݱͰ͖͍ͯͳ͍࣮ࡍɺ͜ͷσʔλΛ୯ճؼϞσϧͰֶश͢ΔࡍʹϕΠζඞཁͳ͍ʢ୯ճؼϞσϧ͕ཧղ͍͔͢͠Β༻͍ͨʣ͔͠͠ɺҰൠʹϕΠζͰߟ͑ΔϝϦοτ͕ଟ͍14
ϕΠζͷಛw ύϥϝʔλʢ୯ճؼϞσϧͳΒ ʣʹ͍ͭͯ֬Λߟ͑ΒΕΔw ࣄલʹʢσʔλҎ֎ͷʣطͷใΛөͤ͞ΒΕΔw ֬ͷஞ࣍ߋ৽͕Ͱ͖Δw աֶशΛ͛Δʢਖ਼ଇԽʣw ʢଞʹ৭ʑ͋Δͱࢥ͍·͢ʣw15
͝ਗ਼ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠16