The lecture introduces the mathematical tools for modeling high-dimensional data, in connection with statistical physics and information theory. Statistical physics shows that macroscopic laws result from the statistics of microscopic particle interactions. This is captured by the system's energy and entropy.
Information theory provides a mathematical definition of the entropy of a probability distribution, which is related to the size of an optimal data code. Markov chain modeling defines models of temporal evolution, including entropy increase.
The maximum entropy principle is used to model high-dimensional data, with probability distributions specified by a limited number of parameters. They define a Gibbs energy as in statistical physics. Non-Gaussian distributions can be constructed, whose properties are captured by scale separation, by characterizing scale interactions. The lecture looks at applications for modeling and generating physical fields and images.