Description
Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology – communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes – the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
- Readable, fun and enthusiastic introduction to a dynamic and exciting field
- Covers theory and applications in tandem, including discussion of state-of-the-art codes used in data compression, error correction and learning; and Bayesian models and Monte Carlo methods
- Contains lots of worked examples and exercises, many of which have full solutions in the book
Table of Contents
1. Introduction to information theory
2. Probability, entropy and inference
3. More about inference
Part I. Data Compression:
4. The source coding theorem
5. Symbol codes
6. Stream codes
7. Codes for integers
Part II. Noisy-Channel Coding:
8. Dependent random variables
9. Communication over a noisy channel
10. The noisy-channel coding theorem
11. Error-correcting codes and real channels
Part III. Further Topics in Information Theory:
12. Hash codes
13. Binary codes
14. Very good linear codes exist
15. Further exercises on information theory
16. Message passing
17. Constrained noiseless channels
18. Crosswords and codebreaking
19. Why have sex? Information acquisition and evolution
Part IV. Probabilities and Inference:
20. An example inference task: clustering
21. Exact inference by complete enumeration
22. Maximum likelihood and clustering
23. Useful probability distributions
24. Exact marginalization
25. Exact marginalization in trellises
26. Exact marginalization in graphs
27. Laplace’s method
28. Model comparison and Occam’s razor
29. Monte Carlo methods
30. Efficient Monte Carlo methods
31. Ising models
32. Exact Monte Carlo sampling
33. Variational methods
34. Independent component analysis
35. Random inference topics
36. Decision theory
37. Bayesian inference and sampling theory
Part V. Neural Networks:
38. Introduction to neural networks
39. The single neuron as 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
Part VI. Sparse Graph Codes
47. Low-density parity-check codes
48. Convolutional codes and turbo codes
49. Repeat-accumulate codes
50. Digital fountain codes
Part VII. Appendices: A. Notation
B. Some physics
C. Some mathematics
Bibliography
Index.
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