Near optimal sample complexity for matrix and tensor normal models via geodesic convexity

1 code implementation • 14 Oct 2021 • Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter

For the matrix normal model, all our bounds are minimax optimal up to logarithmic factors, and for the tensor normal model our bound for the largest factor and overall covariance matrix are minimax optimal up to constant factors provided there are enough samples for any estimator to obtain constant Frobenius error.

Barriers for recent methods in geodesic optimization

no code implementations • 12 Feb 2021 • Cole Franks, Philipp Reichenbach

We study a class of optimization problems including matrix scaling, matrix balancing, multidimensional array scaling, operator scaling, and tensor scaling that arise frequently in theory and in practice.

Computational Complexity Combinatorics Optimization and Control Primary: 68Q17, Secondary: 05Dxx, 05E10, 14Q20, 20G05