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We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal

We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…

Data Structures and Algorithms · Computer Science 2021-07-13 Arun Jambulapati , Yin Tat Lee , Jerry Li , Swati Padmanabhan , Kevin Tian

We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but…

Computation · Statistics 2021-04-13 Pierre Gloaguen , Sylvain Le Corff , Jimmy Olsson

We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…

Data Structures and Algorithms · Computer Science 2024-12-06 Sayan Bandyapadhyay , William Lochet , Daniel Lokshtanov , Dániel Marx , Pranabendu Misra , Daniel Neuen , Saket Saurabh , Prafullkumar Tale , Jie Xue

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…

Algebraic Topology · Mathematics 2008-12-09 Gregor Jerse , Neza Mramor Kosta

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Artificial Intelligence · Computer Science 2012-12-12 David Ephraim Larkin

Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…

Data Structures and Algorithms · Computer Science 2020-03-13 Soheil Behnezhad , Laxman Dhulipala , Hossein Esfandiari , Jakub Łącki , Vahab Mirrokni

We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…

Probability · Mathematics 2024-12-12 Madhur Tulsiani , June Wu

Purpose: To develop a general framework for Parallel Imaging (PI) with the use of Maxwell regularization for the estimation of the sensitivity maps (SMs) and constrained optimization for the parameter-free image reconstruction. Theory and…

Image and Video Processing · Electrical Eng. & Systems 2020-08-21 Matteo Alessandro Francavilla , Stamatios Lefkimmiatis , Jorge F. Villena , Athanasios G. Polimeridis

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

Computation · Statistics 2019-11-28 N. Benjamin Erichson , Sergey Voronin , Steven L. Brunton , J. Nathan Kutz

Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…

Machine Learning · Computer Science 2026-05-25 Ziwen Liu , Meng Li

We address the problem of parameter estimation for degenerate diffusion processes defined via the solution of Stochastic Differential Equations (SDEs) with diffusion matrix that is not full-rank. For this class of hypo-elliptic diffusions…

Statistics Theory · Mathematics 2024-09-04 Yuga Iguchi , Alexandros Beskos

A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to…

Combinatorics · Mathematics 2008-07-02 Sven Herrmann , Michael Joswig

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…

Computational Complexity · Computer Science 2016-10-26 Gábor Braun , Samuel Fiorini , Sebastian Pokutta

In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…

Statistics Theory · Mathematics 2015-10-20 Minwoo Chae

The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…

Data Structures and Algorithms · Computer Science 2025-07-03 Kristóf Bérczi , Karthekeyan Chandrasekaran , Tamás Király , Daniel P. Szabo

Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In…

Statistics Theory · Mathematics 2014-11-06 Sébastien Gadat , Thierry Klein , Clément Marteau

We initiate a study of when the value of mathematical relaxations such as linear and semidefinite programs for constraint satisfaction problems (CSPs) is approximately preserved when restricting the instance to a sub-instance induced by a…

Computational Complexity · Computer Science 2010-05-03 Boaz Barak , Moritz Hardt , Thomas Holenstein , David Steurer

We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using…

Numerical Analysis · Mathematics 2022-07-21 Jess Banks , Jorge Garza-Vargas , Archit Kulkarni , Nikhil Srivastava

To explain the decision of any model, we extend the notion of probabilistic Sufficient Explanations (P-SE). For each instance, this approach selects the minimal subset of features that is sufficient to yield the same prediction with high…

Machine Learning · Statistics 2022-10-17 Salim I. Amoukou , Nicolas J. B Brunel