Prml sec3

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PRML Section3.

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Prml sec3

  1. 1. PRML §3 2010 / 06 / 27 id: taki0313 2010 7 9
  2. 2. CONTENTS ● §3.1 ● §3.2 ● §3.3 ● §3.4 ● §3.5 ● §3.6 2010 7 9
  3. 3. Introduction ● → ● {xn} , {tn} x t … t = y(x) p( t | x ) … Et[t | x] @ §1.5.5 2010 7 9
  4. 4. §3.1 ● ● Φj w Φj(x) = x^j 2010 7 9
  5. 5. 2010 7 9
  6. 6. §3.1.1 ● + ● ● : y(x,w) 2010 7 9
  7. 7. N 2010 7 9
  8. 8. ED : =0 2010 7 9
  9. 9. …? 2010 7 9
  10. 10. M=3, N=2 /// 2010 7 9
  11. 11. 2010 7 9
  12. 12. 2010 7 9
  13. 13. w0 β 2010 7 9
  14. 14. §3.1.2 ● N ● M=2, N=3 j N Φ j Φ(xn) n 2010 7 9
  15. 15. ●N>M M S ●t y(xn,w) ∈ S = 3.2 … 2010 7 9
  16. 16. §3.1.3 ● ● E τ η (3.12)ED … LMS ( ) 2010 7 9
  17. 17. §3.1.4 ● λ … 2010 7 9
  18. 18. ● ● ● q=1(lasso) λ → 2010 7 9
  19. 19. ● … λ → M →λ …? ? §3.4 ● 2 2010 7 9
  20. 20. §3.1.5 ● y :K W : (M,K) 2010 7 9
  21. 21. ● tk n tnk,N 2010 7 9
  22. 22. §3.2 ● §1.5.5 p(t|x) … … ● h(x) y ( !) 2010 7 9
  23. 23. ∞ … h(x) y(x,w) …? = w D 2010 7 9
  24. 24. ● D 2*(...) ( )^2 Bias: Variance: 2010 7 9
  25. 25. ● … = Bias^2 + Variance + Noise Bias Variance Bias - Variance h(x) = sin(2πx) , N=25 , M=25 100 λ 2010 7 9
  26. 26. ● … & ! 2010 7 9
  27. 27. §3.3 ● ● w … 2010 7 9
  28. 28. w 2 w ∝ × ?→2 w mN 2010 7 9
  29. 29. ∞ mN WML … 2010 7 9
  30. 30. @ (ry 2010 7 9
  31. 31. ●1 x, 1 t, y(x,w) = w0 + x*w1 ● f(x, a) = a0 + x*a1 (a0=-0.3, a1=0.5) xn ∈ U(x| -1, 1) f(xn, a) σ=0.2 tn ● : a0=-0.3 , a1=0.5 ● α=2.0 β=(1 / 0.2)^2 = 25 ( ) ● ∝ * ●w p(w|α)=N(w|0,1/αE) 2010 7 9
  32. 32. y(x,w) 1 ( ) 2 ( ) w … 2010 7 9
  33. 33. q=2 q=2 … w = 2010 7 9
  34. 34. §3.3.2 ● t → ● ?2 k& & 1/β + w N→∞ →0 (w ) 2010 7 9
  35. 35. @ 2010 7 9
  36. 36. ● sin(2πx) , N = 1 , 2 , 4 , 25. , ● ± ● 9 ●w y(x,w) 2010 7 9
  37. 37. §3.3.3 ● 2010 7 9
  38. 38. … k(x,x’) : x’ , x k(x,x’) x x’ x‘ 2010 7 9
  39. 39. y(x) y(x’) : k(x,x’) 2010 7 9
  40. 40. §3.4 ● L {Mi} D P(Mi) D 2010 7 9
  41. 41. p(Mi) : p(D|Mi) : ? p(D|Mi) / p(D|Mj) : ( ) 2010 7 9
  42. 42. ● w w 1 2010 7 9
  43. 43. p(w) ~ 1 / Δwprior : wMAP Δwposterior w ( ) 2010 7 9
  44. 44. M : + M … M1 M2 M3 2010 7 9
  45. 45. D p(w) w p(D|w) M1 : D M3 : D p(D|Mi) D0 M2 M1 D0 M3 D0 2010 7 9
  46. 46. M D ? 2 M1, M2. M1 D 2010 7 9
  47. 47. §3.5 ● α,β … w 2 … 2010 7 9
  48. 48. :w α β p(t|w,β) : (3.8) , p(w|t,α,β) : (3.49),(3.53),(3.54) p(α,β|t) α β α β w 2010 7 9
  49. 49. α,β p(t|α,β) α,β EM 2010 7 9
  50. 50. §3.5.1 ● p(t|α,β) (3.11), (3.12), (3.52) … 2010 7 9
  51. 51. 2010 7 9
  52. 52. (3.27) w A ∇∇E(w) : A mN 2010 7 9
  53. 53. 2010 7 9
  54. 54. ● M ● α = 5 * 10^{-3} ● 3~8 3 ● M=3 2010 7 9
  55. 55. §3.5.2 ● p(t|α,β) α ● →A α + λi ● ln |A| α 2010 7 9
  56. 56. α 2α &Σ M α … 2010 7 9
  57. 57. α → β γ, mN α α →γ,mN →α →… × β → λi β λi β 2010 7 9
  58. 58. §3.5.3 ● α ● → ● λi 2010 7 9
  59. 59. λ γ γ well-determined λ1 < λ2 λ2 λ1 γ← γ → γ: γ → → Wml 2010 7 9
  60. 60. β 1 μML γ γ → 1 / N-γ 2010 7 9
  61. 61. ● +9 M=10 ●β 11.1 α ● γ 2αEw(mn) ● ● α ● 2010 7 9
  62. 62. ● γ ● 0≦α≦∞ → 0≦γ≦M {wi} α→γ γ→ α ● M << N well-determined ● ●α β … 2010 7 9
  63. 63. §3.6 ● → ● ● ● 1. 2. →M ● 1. 2. 2010 7 9

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