Spike Wigner Model

This lecture delves into the Spike Wigner model, focusing on the concept of a Digner spike matrix and its perturbation. The instructor explains the implications of observing matrices in this model, the fundamental theorems related to quantum matrices, and the phase transition phenomenon. The lecture also covers the Bayesian denoising approach, the state evolution, and the analysis of the optimal denoiser. The discussion extends to the VESA phenomenon, the fixed points of algorithms, and the comparison between spectral methods and Bayesian approaches in terms of mean square error. The lecture concludes with a look at the phase diagram for the optimal denoiser and the implications of signal sparsity in machine learning.