Abstract

Reconstructing, or generating, high dimensional distributions starting from data is a central problem in machine learning and data sciences. I will present a method —The Wavelet Conditional Renormalization Group —that combines ideas from physics (renormalization group theory) and computer science (wavelets, stable representations of operators). The Wavelet Conditional Renormalization Group allows to reconstruct in a very efficient way classes of high dimensional probability distributions hierarchically from large to small spatial scales, and to perform RG directly from data. It allows to bridge the gap between approaches based on physical intuition and modern machine learning algorithms. I will present the method and then show its applications to data from statistical physics and cosmology. I shall also discuss the interesting insights that our method offers on the interplay between structures of data and architectures of deep neural networks.