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Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…

Quantum Physics · Physics 2016-10-25 Sevag Gharibian , Julia Kempe

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

Quantum Physics · Physics 2024-09-02 Bernardo Ameneyro , Rebekah Herrman , George Siopsis , Vasileios Maroulas

We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…

Computational Geometry · Computer Science 2014-11-27 Rinat Ben-Avraham , Matthias Henze , Rafel Jaume , Balázs Keszegh , Orit E. Raz , Micha Sharir , Igor Tubis

We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given…

Data Structures and Algorithms · Computer Science 2015-11-13 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

Let $T=t_0 ... t_{n-1}$ be a text and $P = p_0 ... p_{m-1}$ a pattern taken from some finite alphabet set $\Sigma$, and let $\dist$ be a metric on $\Sigma$. We consider the problem of calculating the sum of distances between the symbols of…

Data Structures and Algorithms · Computer Science 2008-02-12 Klim Efremenko , Ely Porat

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

Information Theory · Computer Science 2024-05-01 Fernando Hernando , Francisco D. Igual , Gregorio Quintana-Ortí

We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…

Machine Learning · Statistics 2019-12-10 Shubhanshu Shekhar , Tara Javidi , Mohammad Ghavamzadeh

In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be…

Machine Learning · Statistics 2023-05-25 Ying Huang , Liang Chen

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

Probability · Mathematics 2019-11-14 Marie Ernst , Yvik Swan

We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…

Data Structures and Algorithms · Computer Science 2022-03-04 Amir Abboud , Vincent Cohen-Addad , Euiwoong Lee , Pasin Manurangsi

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

Mathematical Physics · Physics 2009-10-20 Nikola Zlatanov , Ljupco Kocarev

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

Computation · Statistics 2020-12-17 Max Sommerfeld , Jörn Schrieber , Yoav Zemel , Axel Munk

We consider a problem which has received considerable attention in systems literature because of its applications to routing in delay tolerant networks and replica placement in distributed storage systems. In abstract terms the problem can…

Data Structures and Algorithms · Computer Science 2013-07-16 Constantinos Daskalakis , Anindya De , Ilias Diakonikolas , Ankur Moitra , Rocco A. Servedio

The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…

Computational Geometry · Computer Science 2022-05-03 Kyle Fox , Jiashuai Lu

This paper presents a novel way to approximate a distribution governing a system of coupled particles with a product of independent distributions. The approach is an extension of mean field theory that allows the independent distributions…

Statistical Mechanics · Physics 2007-05-23 David H. Wolpert

The paper studies upper bounds for the total variation distance between two polynomials of a special form in random vectors satisfying the Doeblin-type condition. Our approach is based on the recent results concerning Nikolskii--Besov-type…

Probability · Mathematics 2023-08-07 Egor Kosov , Anastasia Zhukova

Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex…

Numerical Analysis · Mathematics 2019-03-27 Fenglong Qu , Haiwen Zhang

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…

Optimization and Control · Mathematics 2021-06-03 Shu Liu , Haodong Sun , Hongyuan Zha

We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…

Data Structures and Algorithms · Computer Science 2021-05-06 Zdeněk Dvořák , Abhiruk Lahiri

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Pierre-François Marteau , Gilbas Ménier