20 papers
Revisiting column subset selection through the lens of submodularity
Ilse C. F. Ipsen, Arvind K. Saibaba
The paper shows that the logarithm of the volume of a set of matrix columns is a submodular function, allowing classic QR with column pivoting to be viewed as a greedy algorithm wi…
A Majorization-Minimization with Monte Carlo Approach for Hyperparameter Estimation
Elle Buser, Julianne Chung, Hugo DÃaz +1
We consider inverse problems with linear forward models and Gaussian priors, but with unknown hyperparameters that may arise from the model, the noise, or the specification of the…
Many (most?) column subset selection criteria are NP hard for a few columns
Ilse C. F. Ipsen, Arvind K. Saibaba
We consider a variety of criteria for selecting k representative columns from a real mxn matrix A, when sufficiently few columns are required, i.e., 1<= k<= min{rank(A), m/3}. The…
Improved Analysis of Khatri-Rao Random Projections and Applications
Arvind K. Saibaba, Bhisham Dev Verma, Grey Ballard
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prev…
FlexTrace: Exchangeable Randomized Trace Estimation for Matrix Functions
Madhusudan Madhavan, Alen Alexanderian, Arvind K. Saibaba
We consider the task of estimating the trace of a matrix function, , of a large symmetric positive semi-definite matrix . This problem arises in mult…
Multifidelity sensor placement in Bayesian state estimation problems
Gabriela Ramon, Geena Sarnoski, Vasishta Tumuluri +2
We study optimal sensor placement for Bayesian state estimation problems in which sensors vary in cost and fidelity, resulting in a budget-constrained multifidelity optimal experim…