i , y) ͷΑ͏ʹະύϥϝʔλ θy i Ͱ͔͚͍ͯΔͱ͢Δɻθy i ޙड़ͷଟ߲ ͷྫͰ͋Εɺ໎ϝʔϧྨͷ i ൪ͷޠͷग़ݱ֬ʹ૬͢Δɻ ର log ͷதͷੵ͕ͦΕͧΕͷͰॻ͚ͯɺ͞Βʹ n ʹ͍ͭͯ·ͱΊ͋͛ΔͱҎԼʹͳΔɻ L(Θ | D) = N ∑ n=1 M ∑ i=1 ln p(x(n) i | θy(n) i , y(n)) = M ∑ i=1 { ∑ n∈D1 ln p(x(n) i | θ1 i , y = 1) + ∑ n∈D0 ln p(x(n) i | θ0 i , y = 0) } (3.2) ͨͩ͠ɺD0 y(n) = 0 ͱͳΔඪຊͷू߹,D1 y(n) = 1 ͱͳΔඪຊͷू߹. ͜ΕΑΓ θ1 i ͷ࠷ղΛ༩͑Δ݅ҎԼɻ 0 = ∂L ∂θ1 i = ∂ ∂θ1 i ∑ n∈D1 ln p(x(n) i | θ1 i , y = 1) ղऍ ࠷ӈลʹɺมͷఴࣈ i ͱ y = 1 ʹରԠ͢Δ߲͔͠Βͳ͍ɻ ͜Εɺ3.1 ͕Γཱͭͱ͖ʹɺม i ͝ͱ,y ͝ͱʹΓ͚ΒΕͨͱ͍͏͜ͱΛҙຯ͢Δɻ @functionalaho ҟৗݕͱมԽݕ ྠߨձ 2016-3-17 2016-3-31 8 / 32
܇࿅σʔλʹͳ͍୯ޠͷ͕֬θϩͱͳΓܭࢉͰ͖ͳ͍ ରॲ๏ εϜʔδϯά (smoothing) ͱ͍͏ԼବΛཤ͔ͤΔख๏Λ͏ɻ ͨͱ͑ɺN(y) i → N(y) i + γ(γ > 0) (ςΩετޡ২?) ͱஔ͖͑ͯɺ ˆ θy i = Ny i + γ |Dy| + Mγ (3.8) ͨͩ͠, ∑ n x(n) i = Ny i , ∑ i N(y) i = |Dy|. શ୯ޠͰੵ͢ΔͱͪΌΜͱ 1 ʹͳ͍ͬͯΔ. M ∑ i=1 θy i = ∑ i Ny i + Mγ |Dy| + Mγ = |Dy| + Mγ |Dy| + Mγ @functionalaho ҟৗݕͱมԽݕ ྠߨձ 2016-3-17 2016-3-31 21 / 32