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 distributions hierarchically from large to small spatial scales. I will present the method and then show its applications to data from statistical physics and cosmology. The Wavelet Inverse Renormalization Group Method also provides interesting insights on the interplay between structures of data and architectures of deep neural networks.

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