Information Theory, Inference, and Learning Algorithms phần 3 pdf

... message length. Solution to exercise 6 .3 (p.118). The standard method uses 32 random bits per generated symbol and so requires 32 000 bits to generate one thousand samples. Arithmetic coding uses ... the mutual information is: I(X; Y ) = H(Y ) − H(Y |X) (9 .30 ) = H 2 (0.5) − H 2 (0.15) (9 .31 ) = 1 − 0.61 = 0 .39 bits. (9 .32 ) Solution to exercise 9.8 (p.150). We again compute the m...

Ngày tải lên: 13/08/2014, 18:20

... book for 30 pounds or $50. See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links. 542 45 — Gaussian Processes 3. 0 −1.0 1.0 3. 0 5.0 x −2.0 −1.0 0.0 1.0 2.0 3. 0 t 3. 0 −1.0 1.0 3. 0 5.0 x −4.0 −2.0 0.0 2.0 4.0 t (a) ... exp  − (x−x  ) 2 2(1.5) 2  (b) 2 exp  − (x−x  ) 2 2(0 .35 ) 2  3. 0 −1.0 1.0 3. 0 5.0 x −4.0 −2.0 0.0 2.0 4.0 t 3. 0 −1.0 1.0 3. 0 5.0 x −4.0 −2.0 0....

Ngày tải lên: 13/08/2014, 18:20

... are P (r = 3 |f,N = 3) and P (r = 2 |f,N = 3) .] p b = p B = 3f 2 (1 − f) + f 3 = 3f 2 − 2f 3 . (1 .36 ) This probability is dominated for small f by the term 3f 2 . See exercise 2 .38 (p .39 ) for further ... Methods 30 Efficient Monte Carlo Methods 31 Ising Models 32 Exact Monte Carlo Sampling 33 Variational Methods 34 Independent Component Analysis 35 Random Inference T...

Ngày tải lên: 13/08/2014, 18:20

... (H i ) P (D = 3) (3. 38) P (H 1 |D = 3) = (1/2)(1 /3) P (D =3) P (H 2 |D = 3) = (1)(1 /3) P (D =3) P (H 3 |D = 3) = (0)(1 /3) P (D =3) (3. 39) The denominator P (D = 3) is (1/2) because it is the normalizing ... figure 5 .3? When we say ‘optimal’, let’s assume our aim is to x P (x) a 0.0575 b 0.0128 c 0.02 63 d 0.0285 e 0.09 13 f 0.01 73 g 0.0 133 h 0. 031 3 i 0.0599 j 0.00...

Ngày tải lên: 13/08/2014, 18:20

... rates: Checks, M (N, K) R = 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.2 23] What is the probability ... for links. 13. 2: Obsession with distance 207 w A(w) 0 1 5 12 8 30 9 20 10 72 11 120 12 100 13 180 14 240 15 272 16 34 5 17 30 0 18 200 19 120 20 36 Total 2048 0 50 100 1...

Ngày tải lên: 13/08/2014, 18:20

... by x = x 1 x 2 x 3 . . . = c 1 (u 1 )c 2 (u 2 )c 3 (u 3 ) . . . (18.17) and y = y 1 y 2 y 3 . . . = c  1 (v 1 )c  2 (v 2 )c  3 (v 3 ) . . . , (18.18) where the codes c t and c  t are two ... and variational methods (Chapter 33 ); and 2. Monte Carlo methods – techniques in which random numbers play an integral part – which will be discussed in Chapters 29, 30 , and...

Ngày tải lên: 13/08/2014, 18:20

... links. 23. 3: Distributions over positive real numbers 31 3 and n is called the number of degrees of freedom and Γ is the gamma function. If n > 1 then the Student distribution ( 23. 8) has a mean and ... x 3 } denoted by x m in the general function (26.1) are here x 1 = {x 1 }, x 2 = {x 2 }, x 3 = {x 3 }, x 4 = {x 1 , x 2 }, and x 5 = {x 2 , x 3 }. 33 4 Copyright Cambri...

Ngày tải lên: 13/08/2014, 18:20

... 2.5 3 3.5 4 4.5 5 sd of Energy 0.015 0.02 0.025 0. 03 0. 035 0.04 0.045 0.05 2 2.5 3 3.5 4 4.5 5 (c) 0 0.2 0.4 0.6 0.8 1 2 2.5 3 3.5 4 4.5 5 Mean Square Magnetization 0 0.2 0.4 0.6 0.8 1 2 2.5 3 3.5 ... pounds or $50. See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links. 37 6 29 — Monte Carlo Methods 1 2 3a,3b,3c 3d,3e 5,6 8 5,6,7 Figure 29.16. Slice sampling. Each panel...

Ngày tải lên: 13/08/2014, 18:20

... links. 446 35 — Random Inference Topics Now, 2 10 = 1024  10 3 = 1000, so without needing a calculator, we have 1 2 3 4 5 6 7 8 9 10 ✻ ❄ P (1) ✻ ❄ P (3) ✻ ❄ P (9) 10 log 2  3 log 10 and p 1  3 10 . ... (37 .11) The likelihood function is P ({F i }|p A+ , p B+ ) =  N A F A+  p F A+ A+ p F A− A−  N B F B+  p F B+ B+ p F B− B− (37 .12) =  30 1  p 1 A+ p 29 A−  10 3  p...

Ngày tải lên: 13/08/2014, 18:20

... cyclic codes N 7 21 73 2 73 1057 4161 M 4 10 28 82 244 730 K 3 11 45 191 8 13 3 431 d 4 6 10 18 34 66 k 3 5 9 17 33 65 0.0001 0.001 0.01 0.1 1 1.5 2 2.5 3 3.5 4 Gallager(2 73, 82) DSC(2 73, 82) Figure 47.18. ... Lectures, pp. 35 3 36 8. Springer. Baum, E., Boneh, D., and Garrett, C. (1995) On genetic algorithms. In Proc. Eighth Annual Conf. on Computational Learning Theory...

Ngày tải lên: 13/08/2014, 18:20