Abstract
The curse of high dimensionality results from the Combinatorics explosion of the set of possible models when there is a large number of variables. This explosion is avoided by introducing constraints on probabilistic models. Markov chain and field models limit the number of possible interactions between variables, with conditional independence constraints. This makes it possible to factor probability distributions with simpler conditional probabilities. Links with maximum entropy models are discussed.
The second part of the lecture introduces the two principles of thermodynamics, within the framework of the kinetic theory of gases, which form the basis of statistical physics. These two principles are the conservation of energy and the entropy increase of isolated systems, which is linked to the notion of irreversibility.
