Parameter estimation in linear sparse regression

Pierre Barbault (IRAP)

What do the radial velocity of a star, a spectral mixture and the electromagnetic field produced by the brain have in common? 

In all three cases, one might describe the data as a linear combination of a small number of elementary signals, sometimes called ‘atoms’ (sinusoids, spectra, peaks, dipoles, etc.). 
Introduced in the 1990s, sparse regression consists of finding the smallest combination of these elements that fits to the measurements. The use of random variables to select atoms has given rise to various methods and algorithms (LASSO, MCMC, CHAMPAGNE, etc.). More specifically, focus has been placed on the Bernoulli-Gaussian distribution to model data sparsity. However, the parameters of these distributions (for both atoms and noise) are often either assumed to be known or remain to be estimated as a by-product of the source regression. In this talk, I will introduce a family of methods for the unsupervised estimation of these model parameters in the case of large-scale linear problems.