Unsupervised Learning from Max Entropy to Deep Generative Networks

Generative convolutional networks have obtained spectacular results to synthesize complex signals such as images, speech, and music, with barely any mathematical understanding. This lecture will move towards this world by beginning from well, relatively understood maximum entropy modelization. We first show that non-Gaussian and non-Markovian stationary processes requires to separate scales and measure scale interactions, which can be done with a deep neural network. Applications to turbulence models in physics and cosmology will be shown. We shall review deep generative networks such as GAN and variational encoders, which can synthesize realizations of non-stationary processes or highly complex processes such as speech or music. We show that they can be considerably simplified by defining the estimation as an inverse problem. This will build a bridge with maximum entropy estimation. Applications will be shown on images, speech and music generation.