相关论文: New Constructive Aspects of the Lovasz Local Lemma

A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…

Stochastic local search (SLS) is a successful paradigm for solving the satisfiability problem of propositional logic. A recent development in this area involves solving not the original instance, but a modified, yet logically equivalent…

The Lov\'asz hinge is a convex loss function proposed for binary structured classification, in which k related binary predictions jointly evaluated by a submodular function. Despite its prevalence in image segmentation and related tasks,…

We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal…

Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy. Our primary focus is on extending the existing…

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…

We present polynomial-time algorithms for approximate counting and sampling solutions to constraint satisfaction problems (CSPs) with atomic constraints within the local lemma regime: $$ pD^{2+o_q(1)}\lesssim 1. $$ When the domain size $q$…

Lagarias and Odlyzko (J.~ACM~1985) proposed a polynomial time algorithm for solving ``\emph{almost all}'' instances of the Subset Sum problem with $n$ integers of size $\Omega(\Gamma_{\text{LO}})$, where $\log_2(\Gamma_{\text{LO}}) > n^2…

We study an algorithm for approximating the multivariate independence polynomial $Z(\mathbf{z})$, with negative and complex arguments, an object that has strong connections to combinatorics and to statistical physics. In particular, the…

We give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We…

The regularity lemma of Szemeredi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. In some applications however, one would like to have a strong control on how quasi-random these bipartite…

Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Large Language Models (LLMs) harness extensive data from the Internet, storing a broad spectrum of prior knowledge. While LLMs have proven beneficial as decision-making aids, their reliability is hampered by limitations in reasoning,…