Information Theory, Inference, and Learning Algorithms phần 4 potx

... 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.223] What is the probability of block error ... distribution is Normal(0, v + σ 2 ), since x and the noise are independent random variables, and variances add for independent random variables. The mutual information is: I(X; Y ) = ...

Ngày tải lên: 13/08/2014, 18:20

... a Classifier 40 Capacity of a Single Neuron 41 Learning as Inference 42 Hopfield Networks 43 Boltzmann Machines 44 Supervised Learning in Multilayer Networks 45 Gaussian Processes 46 Deconvolution VI ... a Classifier 40 Capacity of a Single Neuron 41 Learning as Inference 42 Hopfield Networks 43 Boltzmann Machines 44 Supervised Learning in Multilayer Networks 45 Ga...

Ngày tải lên: 13/08/2014, 18:20

... 0.00 84 6.9 7 1010000 l 0.0335 4. 9 5 11101 m 0.0235 5 .4 6 110101 n 0.0596 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 0.0508 4. 3 5 11011 s 0.0567 4. 1 4 0011 t ... function 0 10 20 30 40 50 0 0.2 0 .4 0.6 0.8 1 1.2 1 .4 0 1 2 3 4 5 0 0.2 0 .4 0.6 0.8 1 1.2 1 .4 0 0.1 0.2 0.3 0 .4 0.5 0 0.2 Figure 4. 15. f (x) = x x x x x · · · , s...

Ngày tải lên: 13/08/2014, 18:20

... probability of error when q = 3 64 and K = 1? What is the probability of error when q = 3 64 and K is large, e.g. K = 6000? 9.9 Solutions Solution to exercise 9.2 (p. 149 ). If we assume we observe ... 0.01}: (a) The standard method: use a standard random number generator to generate an integer between 1 and 2 32 . Rescale the integer to (0, 1). Test whether this uniformly distributed...

Ngày tải lên: 13/08/2014, 18:20

... symbols such as ‘x’, and L A T E X commands. 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 to the and of I is Harriet information probability Figure 18 .4. Fit of the Zipf–Mandelbrot distribution (18.10) ... single parthenogenetic mother, K p and the number of children born by a sexual couple, K s . Both (K p = 2, K s = 4) and (K p = 4, K s = 4) are reasonable mod- els. The for...

Ngày tải lên: 13/08/2014, 18:20

... (t n = 0 |y) 1 0.1 0.9 0.061 0.939 2 0 .4 0.6 0.6 74 0.326 3 0.9 0.1 0. 746 0.2 54 4 0.1 0.9 0.061 0.939 5 0.1 0.9 0.061 0.939 6 0.1 0.9 0.061 0.939 7 0.3 0.7 0.659 0. 341 Figure 25.3. Marginal posterior probabilities ... expressing the fraction c = −1/11 = −2/22 = −3/33 = 4/ 44 under this prior, and similarly there are four and two possible solutions for d and e, respectively. So...

Ngày tải lên: 13/08/2014, 18:20

... 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 4 4.5 5 (d) 0 0.2 0 .4 0.6 0.8 1 1.2 1 .4 1.6 2 2.5 3 3.5 4 4.5 5 Heat Capacity 0 0.2 0 .4 0.6 0.8 1 1.2 1 .4 1.6 1.8 2 ... 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....

Ngày tải lên: 13/08/2014, 18:20

... 39) with probability 1 / 4; (x 1 , x 2 ) = (39, 40 ) with probability 1 / 4; (x 1 , x 2 ) = (40 , 39) with probability 1 / 4; (x 1 , x 2 ) = (40 , 40 ) with probability 1 / 4. (37.31) We now consider ... look at a case study: look in depth at exercise 35 .4 (p .44 6) and the reference (Kepler and Oprea, 2001), in which sampling theory estimates and confidence intervals for a m...

Ngày tải lên: 13/08/2014, 18:20

... may fix η and introduce a gain β ∈ (0, ∞) into the activation function: x i = tanh(βa i ). (42 .8) Exercise 42 .2. [1 ] Where have we encountered equations 42 .6, 42 .7, and 42 .8 before? 42 .4 Convergence ... (1997). Multilayer neural networks and Gaussian processes Figures 44 .3 and 44 .2 show some random samples from the prior distribution over functions defined by a selectio...

Ngày tải lên: 13/08/2014, 18:20

... 21 73 273 1057 41 61 M 4 10 28 82 244 730 K 3 11 45 191 813 343 1 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(273,82) DSC(273,82) Figure 47 .18. An algebraically constructed ... 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=2 04 N =40 8 (N=2 04) N=816 N=96 1e-05 0.0001 0.001 0.01 0.1 1 1 1.5 2 2.5 3 3...

Ngày tải lên: 13/08/2014, 18:20