This talk is about efficient solution methods for inverse problems, i.e., the task of recovering an object of interest from known but corrupted data available through a known but possibly corrupted model, formulated in a discrete and linear setting. Since these problems are ill posed, variational regularization methods are often applied to recover a meaningful solution. However, variational...
Non-linearity often leads to slow or unstable convergence in iterative solvers for nonlinear least-squares problems. In this work, we introduce a family of accelerated algorithms that leverage a periodically restarted variant of the Generalized Minimum Residual (GMRES) method to address these challenges. The restarting strategy keeps the computational cost under control and makes the method...
The log-determinant of a symmetric positive semi-definite matrix is a quantity that arises in different contexts, for instance in the evaluation of the log-marginal likelihood for Gaussian processes and in the normalization of the determinantal point processes for supervised learning.
We focus on randomized algorithms for estimating this quantity. The algorithms access the matrix only...
The nearest correlation matrix problem consists in finding the closest valid correlation matrix to a given symmetric matrix that may fail to be positive semi-definite. In other words, given a symmetric unit-diagonal matrix that is not a proper correlation matrix, one seeks the nearest positive semi-definite matrix with unit diagonal entries.
We address the problem of finding the nearest...
