ϊϯύϥϝτϦοΫ๏ w ύϥϝτϦοΫ w ີؔ Ϟσϧ ΛબΜͰɺύϥϝʔλΛσʔλ͔Βਪఆ͢Δ ˠϞσϧ͕σʔλΛද͢ͷʹශऑͩͱɺ༧ଌਫ਼ѱ͍ w ྫ ΨεΛσʔλʹͯΊͯɺЖɾМ?Λਪఆͨ͠ ˠσʔλ͕ଟๆੑͩͱɺΨεͰଊ͑ΒΕͳ͍ w ϊϯύϥϝτϦοΫ w ͷܗঢ়ʹஔ͘Ծఆ͕গͳ͍ w ྫ ଟๆੑͩͱ͔୯ๆੑͳͲͷԾఆஔ͔ͳ͍
ώετάϥϜີਪఆ๏ w ࣍ݩɾ̎࣍ݩఔͷ؆୯ͳՄࢹԽʹཱͭɺ ؆ศͳํ๏ w ͜ͷΞϓϩʔν͔Βɺ࣍ͷ͕̎ͭΘ͔Δ w ͋Δͷ֬ີΛਪఆ͢Δʹɺۙͷ؍ଌͷΛߟྀ͢Δ ඞཁ͕͋Δ w ۠ؒͷ෯େ͖͗ͯ͢ খ͍͚͗ͯ͢͞ͳ͍ w খɿσʔλʹӨڹ͗͢͠Δ w େɿݩͷΛશ͘࠶ݱͰ͖ͳ͍ w ˠϞσϧͷෳࡶ͞ͷબʹࣅ͍ͯΔ
Χʔωϧີਪఆ๏ w ະͷ֬ີQ Y ͔ΒಘΒΕͨ؍ଌू߹Λͬͯɺ Q Y ͷΛਪఆ͍ͨ͠ w YΛؚΉখ͞ͳྖҬ3ͷ֬Λ1ͱ͢Δ ! w /ݸͷ؍ଌ͕ಘΒΕͨͱͯ͠ɺ,ݸͷ؍ଌ͕ 3ʹؚ·ΕΔ֬ɺೋ߲ʹै͏ P = Z R p( x )d x p(K|N, P) = Bin(K|N, P)
Χʔωϧີਪఆ๏ w 7Λݻఆ͠ɺ,Λਪఆ͍ͨ͠ w ֬ີQ Y ΛٻΊ͍ͨΛYɺ؍ଌΛ[email protected]ͱ͢Δ w Ұล͕IͰɺYΛத৺ͱ͢Δখ͞ͳཱํମͷ தʹ͋Δͷ૯ ! w ҰลIͷཱํମͳͷͰɺ7I?%ͱͳΓɺ K = K X n=1 k ✓ x xn h ◆ p( x ) = 1 N K X n=1 1 hD k ✓ x xn h ◆
,ۙີਪఆ๏ w ,Λݻఆ͠ɺ7Λਪఆ͍ͨ͠ w ֬ີQ Y ΛٻΊ͍ͨΛYɺ؍ଌΛ[email protected]ͱ͢Δ w YΛத৺ͱͯ͠ɺ͕,ݸؚ·ΕΔΑ͏ͳٿΛ୳͢ͱ 7Ұҙʹఆ·Γɺ֬ີਪఆ͞ΕΔ ਤXXXPDXUJUFDIBDKQJOEFYQIQ NPEVMF(FOFSBMBDUJPO%PXO-PBEpMF
QEGUZQFDBMΑΓ p( x ) = K NV
,ۙ๏ΛͬͨΫϥεྨ w ϕΠζͷఆཧΑΓɺ ! w ֬ີQ Y ɺઌ΄ͲٻΊͨͱ͓Γ ! w ࣄલɺશͯͷ؍ଌͷ͏ͪΫϥεʹଐ͢Δ؍ଌ ! w ɺͦͷΫϥεʹଐ͢Δ؍ଌͰͷ֬ີΑΓɺ p(Ck | x ) = p( x |Ck)p(Ck) p( x ) p( x ) = K NV p(Ck) = Nk N p( x |Ck) = Kk NkV
,ۙ๏ΛͬͨΫϥεྨ w ϕΠζͷఆཧʹೖ͢Δͱɺ ! w Αͬͯɺ,ۙͷ͏ͪɺΫϥε[email protected]ʹଐ͢ΔͷͰ ଟܾΛऔΕΑ͍ w ಛʹɺ,ͷͱ͖࠷ۙ๏ͱݺΕΔ p(Ck | x ) = p( x |Ck)p(Ck) p( x ) = Kk K ˖ʹ͍ۙ̏ͭͷͰଟܾΛऔ͍ͬͯΔ ࠷ۙ๏Ͱɺ ࠷ۙ๏ͰɺΫϥεͷҟͳΔͷରͷ ਨೋઢʹͳ͍ͬͯΔ