In this work, we address the problem of scalable approximate inference and covariance estimation for linear inverse problems using Expectation-Propagation (EP). Traditional EP methods rely on Gaussian approximations with either diagonal or full covariance structures. Full covariance matrices can capture correlation but do not scale as the dimensions of the problem increases, while diagonal matrices scale better but omit potentially important correlations. For the first time to the best of our knowledge, we propose to investigate low-rank decompositions within EP for linear regression. The potential benefits of such covariance structures are illustrated thorough simulations results obtained on sparse linear regression problems and a more challenging spectral unmixing problem where the sparse mixing coefficients are, in addition, subject to positivity constraints.
|Title of host publication||31st European Signal Processing Conference (EUSIPCO 2023)|
|Publication status||Published - 1 Nov 2023|
|Event||31st European Signal Processing Conference 2023 - Helsinki, Finland|
Duration: 4 Sept 2023 → 8 Sept 2023
|Conference||31st European Signal Processing Conference 2023|
|Abbreviated title||EUSIPCO 2023|
|Period||4/09/23 → 8/09/23|