Related papers: A Sequential Computation Algorithm for the Center …
We present the Continuous Empirical Cubature Method (CECM), a novel algorithm for empirically devising efficient integration rules. The CECM aims to improve existing cubature methods by producing rules that are close to the optimal,…
In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…
In this work, we consider solving optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Sequential Quadratic Programming method to find both first- and second-order stationary…
Horstein, Burnashev, Shayevitz and Feder, Naghshvar et al. and others have studied sequential transmission of a K-bit message over the binary symmetric channel (BSC) with full, noiseless feedback using posterior matching. Yang et al.…
We study the binomial channel and the structure of its capacity-achieving input and output distributions. It is known that the capacity-achieving input distribution is discrete and supported on finitely many points. The best previously…
In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints, called SIPLOG…
We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…
In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects…
The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global…
We consider the classic $k$-center problem {in the constant dimensional Euclidean space} under a parallel setting, on the low-local-space Massively Parallel Computation (MPC) model, with local space per machine of ${O}(n^{\delta})$, where…
Let $P$ be a set of points in some metric space. The approximate furthest neighbor problem is, given a second point set $C,$ to find a point $p \in P$ that is a $(1+\epsilon)$ approximate furthest neighbor from $C.$ The dynamic version is…
Constructing small-sized coresets for various clustering problems in different metric spaces has attracted significant attention for the past decade. A central problem in the coreset literature is to understand what is the best possible…
We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed "space-evolving block decimation" (SEBD) and extends it to the case…
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…
We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value…