チュートリアル:ノンパラメトリックベイズ

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3 { x,x, L, xn} 2 p( θ, θ, θ, θ, θ, } { θ6

4 p( p(

5 { x,x, L, N} 2 x { θ, θ2, θ3, θ4, θ5, θ6} K n p( θ θ n N n θ x N +

6 { x,x, L, N} 2 x { θ, θ2, θ3, θ4, θ5, θ6} log p( 6 n logθ F 6 log p( + λ θ F θ n θ λ 0 θ N n p( θ θ n n λ N λ x K θ 6 θ n N

7 p( p( p(

8 p ( p( θ 3 θ + θ2 + θ3 θ, θ, } Dir( { 2 θ3 θ 2 0 < < 2 0 θ 2 θ 3 {6,2,2} {3,7,5} θ θ {2,3,4} {6,2,6}

9 n Dir( a + n Dir( + n p( p( { 0.4, 0., 0.0, 0.0, 0.2, 0.3} ˆ {0.25, 0.4, 0., 0., 0.8, 0.2}

10 },,,,, { θ θ θ θ θ θ 6 ( n p θ { N} 2 x,,,x x L ( ( Γ Γ ( Dir( ( C p θ θ a 3 a + 6 ( ( ( ( ( ( ( n C p p p p p p θ Dir( ( ( 6 n n n C p θ

11 {, 2, 2,, 2,, 3, 2}

12

13 Dir ( 2 3 L K 2 3 L K K K

14 Dir ( K L L L L L L L L K 0

15 ~ DP(, θ, θ, θ, L, θ } { 2 3 θ

16 ~ θ θ ~ Beta(, ~ ~ θ ( θ l l θ θ 2 Beta(, β θ3 L θ Beta( d, + d Beta(, β ~ θ ~ GEM( ~ ~ θ ~ θ ~ ~ θ θ 2 2 θ3 3

17 { 2 3 θ, θ, θ, Lθ } {, 2, 2,, 2,, p( x p( x p( d next next 3, 2}

18 Dir ( K L L L L K 0 L L L L ( K 4 K

19 { θ, θ2, θ3, Lθ } p( {, 2, 2,, n θ p( DP(, 2,, 3, 2} p( x next x 6 x ( x next x2 x3 2 x4 x 8 x ( x next 2 x ( x next 3 new 8 + ( x next new p( p x p( x p( d ( next next

20

21 p( x π N( x μ, σ 2 p( DP(, G0

22 DP(, {, 2, 2,, 2,, 3, 2} x x2 x3 2 3 x 6 x 4 x 8 x 5 x 7 new DP(, G0 Z {, 2, 2,, 2,, 3, 2} x 2 μ,σ { x, x2, x3, x4, x5, x6, x7, x8} x 6 x 4 p( x x3 μ 3 x 8 2,σ 2 p( μ, σ x 5 L x 7 μ 3,σ G μ, σ 0 new

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