Notes and Comments on S. Mallat’s Lectures at Collège de France (2023)
Résumé
The 2023 course by Stéphane Mallat, Professor at the Collège de France, is a continuation of the 2022 course, focusing on the theme of Entropy. Initially, it delves into Statistical Physics by L. Boltzmann and J. W. Gibbs, and then transitions to Cl. Shannon's Information Theory. To comprehend the Second Law of Thermodynamics, ergodic processes are studied, employing the Shannon–McMillan–Breiman theorem, and Markov chains enable us to demonstrate convergence to equilibrium. We will explore connections with the field of Statistical Learning, through modeling in the context of Maximum Entropy and Gibbs' theorem. Non-Gaussian models are developed, utilizing Harmonic Analysis and the implementation of Scattering networks. Along the way, we will revisit the Fourier Transform and the Wavelet Transform (multiscale analysis).
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