Ͱදݱ͢Δ. Lap(wj|0, 1/γ) = γ 2 e−γ|wj | = N(wj|0, τ2 j )Ga(τ2 j |1, γ2 2 )dτ2 j ͜ΕΛ༻͍Ε, ಉ࣌ p(y, w, τ, σ2|X) = N(y|Xw, σ2IN )N(w|0, Dτ )IG(σ2|aσ, bσ) ⎡ ⎣ j Ga(τ2 j |1, γ2/2) ⎤ ⎦ ∝ (σ2)−N/2 exp − 1 2σ2 ∥y − Xw∥2 2 |D−1/2 τ exp − 1 2 wT Dτ w (σ2)aσ+1 exp(−bσ/σ) j exp(− γ2 2 τ2 j ) ͨͩ͠,Dτ = diag(τ2 j ) Ͱ X ඪ४Խ,y centered ͞Ε͍ͯΔͷͰ offset ߲ແࢹՄೳ. EM ΞϧΰϦζϜͰߟ͑Δ (Figueiredo, 2003) E step: τ2 j , σ2 Λਪఆ͢Δ M step: w ʹؔͯ͠࠷దԽ͢Δ ࣮͜ͷ ˆ w Lasso ਪఆྔͱಉ͡ʹͳΔ Daisuke Yoneoka Sparse linear models October 20, 2014 18 / 21