Title: Proximal approaches for matrix optimization problems (joint work with A. Benfenati and J.C. Pesquet)
Abstract: Various applications such as gene expression, model selection, graph estimation, or brain network analysis all share
very similar matrix variational formulations, namely the minimization, in a symmetric matrix space, of a loss function
decoupled in one term acting only on the eigenvalues of the matrix (e.g., nuclear norm, log-determinant) and another term acting on the matrix elements (e.g., entry-wise l1 norm). This talk will introduce novel proximal and majorization-minimization approaches, to address such convex and non-convex matrix optimization problems, with sound convergence guarantees. The applicability of the proposed schemes will be illustrated on a problem of noisy graphical lasso, where a precision matrix has to be estimated under sparsity constraints in the presence of noise.
Related references:
A. Benfenati, E. Chouzenoux and J.-C. Pesquet. A Proximal Approach for a Class of Matrix Optimization Problems: Application to Robust Precision Matrix Estimation. Tech. Rep., 2019. http://www.optimization-online.org/DB_HTML/2018/01/6431.html
A. Benfenati, E. Chouzenoux and J.-C. Pesquet. A Nonconvex Variational Approach for Robust Graphical Lasso. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018), Calgary, Canada, 15 – 20 April 2018
