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Inference,
and Learning Algorithms
David J.C. MacKay
mackay@mrao.cam.ac.uk
c 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003
Draft 4.0 April 15, 2003
Please send feedback on this book via
http://www.inference.phy.cam.ac.uk/mackay/itprnn/
1
About the exercises
I firmly believe that one can only understand a subject by recreating it for oneself. To this end, I think it is essential to work through some exercises on each topic. For guidance, each exercise has a rating (similar to that used by Knuth (1968)) from 1 to 5 that indicates the level of difficulty. In addition, exercises that are especially recommended are marked by a marginal encouraging rat –
. Exercises that require the use of a computer
may be marked with a C.
Answers to many of the exercises are provided. Please use them wisely. (Where a solution is provided, this is indicated by including the page number of the solution with the difficulty rating.)
Summary of codes for exercises
Especially recommended
[1]
Simple (one minute)
[2]
Medium (quarter hour)
Recommended
[3]
Moderately hard
C
Some parts require a computer
[4]
Hard
[p. 42]
Solution provided on page 42
[5]
Research project
Roadmaps
The diagrams on the following pages will indicate the dependencies between chapters and a few possible routes through the book.
c David J.C. MacKay. Draft 4.0. April 15, 2003
2
1
Introduction to Information Theory
IV Probabilities and Inference
2
Probability, Entropy, and Inference
20
An Example Inference Task: Clustering
3
More about Inference
21
Exact Inference by Complete Enumeration
22
Maximum Likelihood and Clustering
I
Data Compression
23
Useful Probability Distributions
4
The Source Coding Theorem
24
Exact Marginalization
5
Symbol Codes
25
Exact Marginalization in Trellises
6
Stream Codes
26
Exact Marginalization in Graphs
7
An Aside: Codes for Integers
27
Laplace’s Method
28
Model Comparison and Occam’s Razor
II
Noisy-Channel Coding
29
Monte Carlo Methods
8
Correlated Random Variables
30
Efficient Monte Carlo Methods
9
Communication over a Noisy Channel
31
Ising Models
10
The Noisy-Channel Coding Theorem
32
Exact Monte Carlo Sampling
11
Error-Correcting Codes and Real Channels
33
Variational Methods
34
Independent Component Analysis
III Further Topics in Information Theory
35
Random Inference Topics
12
Hash Codes
36
Decision Theory
13
Binary Codes
37
Bayesian Inference and Sampling Theory
14
Very Good Linear Codes Exist
15
Further Exercises on Information Theory
V
Neural networks
16
Message Passing
38
............

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