Bayesian time-frequency representations

This week in lab meeting I presented

Robust spectrotemporal decomposition by iteratively reweighted least squares
Demba Ba, Behtash Babadi, Patrick L Purdon, and Emery N Brown. PNAS, 2014

BaFig1

In this paper, the authors proposed an algorithm for fast, robust estimation of a time-frequency representation.  The robustness properties were achieved by applying a group-sparsity prior across frequencies and a “fused LASSO” prior over time. However, the real innovation that they were able leverage was from an earlier paper, in which the authors proved that the MAP estimation problem could be solved by iteratively re-weighted least squares (IRLS), which turns out to be a version of the EM algorithm.

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