Information Theory, Inference, and Learning Algorithms phần 5 ppsx

... R(f) does 0 1 2 0 0. 25 0 .5 0. 75 1 1+f H_2(f) 0 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0 0. 25 0 .5 0. 75 1 R(f) = H_2(f)/(1+f) Figure 17.1. Top: The information content per source symbol and mean transmitted ... recommend Maynard Smith and Sz´athmary (19 95) , Maynard Smith and Sz´athmary (1999), Kondrashov (1988), May- nard Smith (1988), Ridley (2000), Dyson (19 85) , Cairns-Smith (1...

Ngày tải lên: 13/08/2014, 18:20

... clustering algorithms, and neural networks. Why unify information theory and machine learning? Because they are two sides of the same coin. In the 1960s, a single field, cybernetics, was populated by information ... scientists, and neuroscientists, all studying common problems. Information theory and machine learning still belong together. Brains are the ultimate compression...

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... 4096 (a) -2 -1 .5 -1 -0 .5 0 2 2 .5 3 3 .5 4 4 .5 5 Energy -2 -1 .5 -1 -0 .5 0 2 2 .5 3 3 .5 4 4 .5 5 (b) 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 2 2 .5 3 3 .5 4 4 .5 5 sd of Energy 0.0 15 0.02 0.0 25 0.03 0.0 35 0.04 0.0 45 0. 05 2 ... 5 10 15 20 p (1) (x) 0 5 10 15 20 p (2) (x) 0 5 10 15 20 p (3) (x) 0 5 10 15 20 p (10) (x) 0 5 10 15 20 p (100)...

Ngày tải lên: 13/08/2014, 18:20

... inputs. 1e-06 1e- 05 0.0001 0.001 0.01 0.1 1 1 1 .5 2 2 .5 3 3 .5 4 4 .5 5 5. 5 (N=96) N=204 N=408 (N=204) N=816 N=96 1e- 05 0.0001 0.001 0.01 0.1 1 1 1 .5 2 2 .5 3 3 .5 4 j=3 j=4 j =5 j=6 (a) (b) Figure ... K/S (50 .4) (see figure 50 .2 and exercise 50 .4 (p .59 4)) then add the ideal soliton distribu- tion ρ to τ and normalize to obtain the robust soliton distribution, µ: µ...

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... 0000 b 0.0128 6.3 6 001000 c 0.0263 5. 2 5 00101 d 0.02 85 5.1 5 10000 e 0.0913 3 .5 4 1100 f 0.0173 5. 9 6 111000 g 0.0133 6.2 6 001001 h 0.0313 5. 0 5 10001 i 0. 059 9 4.1 4 1001 j 0.0006 10.7 10 1101000000 k ... 6.9 7 1010000 l 0.03 35 4.9 5 11101 m 0.02 35 5.4 6 110101 n 0. 059 6 4.1 4 0001 o 0.0689 3.9 4 1011 p 0.0192 5. 7 6 111001 q 0.0008 10.3 9 110100001 r 0. 050 8 4.3...

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... 9.7. [1, p. 157 ] Compute the mutual information between X and Y for the binary symmetric channel with f = 0. 15 when the input distribution is P X = {p 0 = 0 .5, p 1 = 0 .5} . Exercise 9.8. [2, p. 157 ] Compute ... |x  )P (x  ) (9. 25) = 0. 15 × 0.1 0. 15 × 0.1 + 0. 85 × 0.9 (9.26) = 0.0 15 0.78 = 0.019. (9.27) Solution to exercise 9.4 (p.149). If we observe y = 0, P (x = 1 |y =...

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... A(w) 0 1 5 12 8 30 9 20 10 72 11 120 12 100 13 180 14 240 15 272 16 3 45 17 300 18 200 19 120 20 36 Total 2048 0 50 100 150 200 250 300 350 0 5 8 10 15 20 25 30 1 10 100 0 5 8 10 15 20 25 30 Figure ... = K/N 2 (3, 1) 1/3 repetition code R 3 3 (7, 4) 4/7 (7, 4) Hamming code 4 ( 15, 11) 11/ 15 5 (31, 26) 26/31 6 (63, 57 ) 57 /63 Exercise 13.4. [2, p.223] What is the prob...

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... http://www.cambridge.org/ 052 1642981 You can buy this book for 30 pounds or $50 . See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links. 358 29 — Monte Carlo Methods (a) 0 0 .5 1 1 .5 2 2 .5 3 -4 -2 0 ... =  1 101  4 101 1 50  4 101 1 50  2 101 1 50  = 0.00000000000 25 = 2 .5 ×10 −12 . (28.3) Thus comparing P(D |H c ) with P (D |H a ) = 0.00010, even if our prior...

Ngày tải lên: 13/08/2014, 18:20

... {1, 0, 3, 0, 0, 5, 0, 5, 0, 6, 107, 0, 0, 0, 1, 0, 0, 64, 0, 35} . [A small amount of computation is required to solve this problem.] 35. 3 Inferring causation Exercise 35. 5. [2, p. 450 ] In the Bayesian ... αm i ) Γ(  i F i + α) Γ(α)  i Γ(αm i ) , ( 35. 13) most factors cancel and all that remains is P (H A→B |Data) P (H B→A |Data) = (7 65 + 1)(2 35 + 1) ( 950 + 1) (50 + 1) = 3.8 1...

Ngày tải lên: 13/08/2014, 18:20

... on this idea by Williams and Rasmussen (1996), Neal (1997b), Barber and Williams (1997) and Gibbs and MacKay (2000), and will assess whether, for supervised regression and classification tasks, ... follows: C N+1 ≡        C N     k    k T  κ       . ( 45. 35) The posterior distribution ( 45. 34) is given by P (t N+1 |t N ) ∝ exp  − 1 2  t N t N+1  C −1 N+1...

Ngày tải lên: 13/08/2014, 18:20