A series of sixteen lectures covering the core of the book "Information Theory, Inference, and Learning Algorithms (Cambridge University Press, 2003)" which can be bought at Amazon, and is available free online. A subset of these lectures used to constitute a Part III Physics course at the University of Cambridge.
Introduction to information theory
* The possibility of reliable communication over unreliable channels. The (7,4) Hamming code and repetition codes.
Entropy and data compression
* Entropy, conditional entropy, mutual information, Shannon information content. The idea of typicality and the use of typical sets for source coding. Shannon's source coding theorem. Codes for data compression. Uniquely decodeable codes and the Kraft-MacMillan inequality. Completeness of a symbol code. Prefix codes. Huffman codes. Arithmetic coding.
Communication over noisy channels
* Definition of channel capacity. Capacity of binary symmetric channel; of binary erasure channel; of Z channel. Joint typicality, random codes, and Shannon's noisy channel coding theorem. Real channels and practical error-correcting codes. Hash codes.
Statistical inference, data modelling and pattern recognition
* The likelihood function and Bayes' theorem. Clustering as an example
Approximation of probability distributions
* Laplace's method. (Approximation of probability distributions by Gaussian distributions.)
* Monte Carlo methods: Importance sampling, rejection sampling, Gibbs sampling, Metropolis method. (Slice sampling, Hybrid Monte Carlo, Overrelaxation, exact sampling)
* Variational methods and mean field theory. Ising models.
Neural networks and content-addressable memories
* The Hopfield network.
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