Related papers: An Approximation Algorithm for l\infty-Fitting Rob…

We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…

We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar $L_1$ type minimization. We use a regularization which…

Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…

Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…

We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…

The current paper studies the problem of minimizing a loss $f(\boldsymbol{x})$ subject to constraints of the form $\boldsymbol{D}\boldsymbol{x} \in S$, where $S$ is a closed set, convex or not, and $\boldsymbol{D}$ is a matrix that fuses…

We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…

In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…

Canonical distances such as Euclidean distance often fail to capture the appropriate relationships between items, subsequently leading to subpar inference and prediction. Many algorithms have been proposed for automated learning of suitable…

This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic…

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor…

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…

Recommender systems inherently exhibit a low-rank structure in latent space. A key challenge is to define meaningful and measurable distances in the latent space to capture user-user, item-item, user-item relationships effectively. In this…

Applications in machine learning and data mining require computing pairwise Lp distances in a data matrix A. For massive high-dimensional data, computing all pairwise distances of A can be infeasible. In fact, even storing A or all pairwise…

Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Given a distance matrix consisting of pairwise distances between species, a distance-based phylogenetic reconstruction method returns a tree metric or equidistant tree metric (ultrametric) that best fits the data. We investigate…

In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…