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We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…

We focus the use of \emph{row sampling} for approximating matrix algorithms. We give applications to matrix multipication; sparse matrix reconstruction; and, \math{\ell_2} regression. For a matrix \math{\matA\in\R^{m\times d}} which…

We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based…

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) for random Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al., where…

We consider the problem of finding an approximate solution to $\ell_1$ regression while only observing a small number of labels. Given an $n \times d$ unlabeled data matrix $X$, we must choose a small set of $m \ll n$ rows to observe the…

Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in…

We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…

A new algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important…

Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and…

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…

We present algorithms for the Max-Cover and Max-Unique-Cover problems in the data stream model. The input to both problems are $m$ subsets of a universe of size $n$ and a value $k\in [m]$. In Max-Cover, the problem is to find a collection…

We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every…

We study the Minimum Latency Submodular Cover problem (MLSC), which consists of a metric $(V,d)$ with source $r\in V$ and $m$ monotone submodular functions $f_1, f_2, ..., f_m: 2^V \rightarrow [0,1]$. The goal is to find a path originating…

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their…

Given a graph $G=(V,E)$ with costs on its edges, the minimum-cost edge cover problem consists of finding a subset of $E$ covering all vertices in $V$ at minimum cost. If $G$ is bipartite, this problem can be solved in time $O(|V|^3)$ via a…

We describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homogenization of multiscale composite materials. An efficient…

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…