相关论文: Average case complexity of linear multivariate pro…

This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We prove that two linesearch-type algorithms enjoy the same…

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…

We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affine-invariant property of…

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…

Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…

The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…

Recent works have demonstrated that the convergence rate of a nonparametric density estimator can be greatly improved by using a low-rank estimator when the target density is a convex combination of separable probability densities with…

LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…

A trigonometrically approximated maximum likelihood estimation for $\alpha$-stable laws is proposed. The estimator solves the approximated likelihood equation, which is obtained by projecting a true score function on the space spanned by…

The complexity of a graph can be obtained as a derivative of a variation of the zeta function or a partial derivative of its generalized characteristic polynomial evaluated at a point [\textit{J. Combin. Theory Ser. B}, 74 (1998), pp.…

We examine the task of locating a target region among those induced by intersections of $n$ halfspaces in $\mathbb{R}^d$. This generic task connects to fundamental machine learning problems, such as training a perceptron and learning a…

The landscape of Large Language Models (LLMs) shifts rapidly towards dynamic, multi-agent systems. This introduces a fundamental challenge in establishing computational trust, specifically how one agent can verify that another's output was…

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…

Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…

We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…

Linear predictors form a rich class of hypotheses used in a variety of learning algorithms. We present a tight analysis of the empirical Rademacher complexity of the family of linear hypothesis classes with weight vectors bounded in…

This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…