In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...
We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a "continuum-of-subspaces" model, a re ...
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...
The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying siz ...
The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure. ...