Information Theory, Inference and Learning AlgorithmsInformation theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering  communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparsegraph codes for errorcorrection. A toolbox of inference techniques, including messagepassing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in errorcorrecting codes, including lowdensity paritycheck codes, turbo codes, and digital fountain codes  the twentyfirst century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for selflearning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning. 
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Review: Information Theory, Inference and Learning Algorithms
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Review: Information Theory, Inference and Learning Algorithms
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Contents
Introduction to Information Theory  3 
Probability Entropy and Inference  22 
ful theoretical ideas of Shannon but also practical solutions to communica  34 
More about Inference  48 
Data Compression  65 
The Source Coding Theorem  67 
Symbol Codes  91 
Stream Codes  110 
Stream Codes 26 I Exact Margmalization in Graphs  346 
Monte Carlo Methods  357 
Efficient Monte Carlo Methods  387 
Ising Models  400 
Exact Monte Carlo Sampling  413 
Variational Methods  422 
Independent Component Analysis and Latent Variable Mod elling  437 
Random Inference Topics  445 
Codes for Integers  132 
NoisyChannel Coding  137 
Dependent Random Variables  138 
Communication over a Noisy Channel  146 
The NoisyChannel Coding Theorem  162 
ErrorCorrecting Codes and Real Channels  177 
Further Topics in Information Theory  191 
Codes for Efficient Information Retrieval  193 
Binary Codes  206 
Very Good Linear Codes Exist  229 
Further Exercises on Information Theory  233 
Message Passing  241 
Communication over Constrained Noiseless Channels  248 
Crosswords and Codebreaking  260 
Why have Sex? Information Acquisition and Evolution  269 
Probabilities and Inference  281 
Clustering  284 
Exact Inference by Complete Enumeration  293 
Maximum Likelihood and Clustering  300 
Useful Probability Distributions  311 
Exact Marginalization  319 
Exact Marginalization in Trellises  324 
Exact Marginalization in Graphs  334 
Laplaces Method  341 
Model Comparison and Occams Razor  343 
Decision Theory  451 
Bayesian Inference and Sampling Theory  457 
Neural networks  467 
Introduction to Neural Networks  468 
The Single Neuron as a Classifier  471 
Capacity of a Single Neuron  483 
Learning as Inference  492 
Hopfield Networks  505 
Boltzmami Machines  522 
Supervised Learning in Multilayer Networks  527 
Gaussian Processes  535 
Deconvolution  549 
Sparse Graph Codes  555 
LowDensity ParityCheck Codes  557 
Convolutional Codes and Turbo Codes  574 
Repeat Accumulate Codes  582 
50 Digital Fountain Codes  588 
Digital Fountain Codes  589 
Appendices  597 
A Notation  598 
B Some Physics  601 
Some Mathematics  605 
613  
620  
Common terms and phrases
approximation arithmetic coding assume average Bayesian binary symmetric channel blocklength capacity Chapter cluster codeword coding theorem compression compute decoding problem defined distance encoding energy ensemble entropy equal equation error probability estimate evaluate example fitness flipped Gaussian channel Gaussian distribution Gibbs sampling given graph Hamming code hash function Huffman code hypothesis independent inference input distribution integer interval Ising model iterations Kmeans algorithm linear code lowdensity paritycheck codes marginal Markov chain maximal mean Metropolis method Monte Carlo methods mutual information neuron node noise level noisy channel normalizing constant obtain optimal outcome output parameters parity paritycheck matrix posterior distribution posterior probability predictions prefix code prior probability density probability distribution probability of error random variable ratio sequence shown in figure shows simulation Solution to exercise source bits space standard deviation string symbol code transmitted trellis typical set uniquely decodeable variance vector weight zero