Information Theory, Inference, and Learning Algorithms phần 7 ppsx
Information Theory, Inference, and Learning Algorithms phần 7 ppsx
... The information learned about P (x) after the algorithm has run for T steps is less than or equal to the information content of a, since all information about P is mediated by a. And the information ... available: X + N arithmetic sum, modulo B, of X and N. X − N difference, modulo B, of X and N. X ⊕ N bitwise exclusive-or of X and N . N := randbits(l) sets N to a random l-bit...
Ngày tải lên: 13/08/2014, 18:20
Information Theory, Inference, and Learning Algorithms phần 1 ppsx
... probabilities that 2, 3, 4, 5, 6, or 7 errors occur in one block. p B = 7 r=2 7 r f r (1 − f) 7 r . (1.46) To leading order, this goes as p B 7 2 f 2 = 21f 2 . (1. 47) (b) The probability of ... 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, c...
Ngày tải lên: 13/08/2014, 18:20
Information Theory, Inference, and Learning Algorithms phần 5 ppsx
... connection matrix. Then C = log 2 λ 1 . ( 17. 16) 17. 4 Back to our model channels Comparing figure 17. 5a and figures 17. 5b and c it looks as if channels B and C have the same capacity as channel A. ... decreasing f . Figure 17. 1 shows these functions; 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...
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Information Theory, Inference, and Learning Algorithms phần 10 ppsx
... links. 47. 7: Fast encoding of low-density parity-check codes 569 difference set cyclic codes N 7 21 73 273 10 57 4161 M 4 10 28 82 244 73 0 K 3 11 45 191 813 3431 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 ... Processing Systems, ed. by D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, volume 8, pp. 75 7 76 3. MIT Press. Amit, D. J., Gutfreund, H., and Sompoli...
Ngày tải lên: 13/08/2014, 18:20
Information Theory, Inference, and Learning Algorithms phần 2 ppt
... 4.3 5 11011 s 0.05 67 4.1 4 0011 t 0. 070 6 3.8 4 1111 u 0.0334 4.9 5 10101 v 0.0069 7. 2 8 11010001 w 0.0119 6.4 7 1101001 x 0.0 073 7. 1 7 1010001 y 0.0164 5.9 6 101001 z 0.00 07 10.4 10 1101000001 – ... a, b, c, d }, and P X = { 1 / 2, 1 / 4, 1 / 8, 1 / 8 }, (5 .7) and consider the code C 3 . The entropy of X is 1 .75 bits, and the expected length L(C 3 , X) of this code is a...
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Information Theory, Inference, and Learning Algorithms phần 3 pdf
... Part II. 6 .7 Exercises on stream codes Exercise 6 .7. [2 ] Describe an arithmetic coding algorithm to encode random bit strings of length N and weight K (i.e., K ones and N −K zeroes) where N and K ... 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 distribu...
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Information Theory, Inference, and Learning Algorithms phần 4 potx
... weight w. The weight enumerator w A(w) 0 1 3 7 4 7 7 1 Total 16 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 Figure 13.1. The graph of the (7, 4) Hamming code, and its weight enumerator function. function ... 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
Information Theory, Inference, and Learning Algorithms phần 6 pptx
... 0.4 0.6 0. 674 0.326 3 0.9 0.1 0 .74 6 0.254 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 for the 7 bits under the ... Plot it, and explore its properties for a variety of data sets such as the one given, and the data set {x n } = {13.01, 7. 39}. [Hint: first find the posterior distribution of σ...
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Information Theory, Inference, and Learning Algorithms phần 8 docx
... ( 37. 5) The expected values of the four measurements are F A+ = 3 ( 37. 6) F A− = 27 ( 37. 7) F B+ = 1 ( 37. 8) F B− = 9 ( 37. 9) and χ 2 (as defined in equation ( 37. 1)) is χ 2 = 5.93. ( 37. 10) Since ... rules and learning rules are invented by imaginative researchers. Alternatively, activity rules and learning rules may be derived from carefully chosen objective fun...
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Information Theory, Inference, and Learning Algorithms phần 9 pdf
... on this idea by Williams and Rasmussen (1996), Neal (1997b), Barber and Williams (19 97) and Gibbs and MacKay (2000), and will assess whether, for supervised regression and classification tasks, ... Gibbs (19 97) . 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 selection of...
Ngày tải lên: 13/08/2014, 18:20