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Generalization error bounds are critical to understanding the performance of machine learning models. In this work, we propose a new information-theoretic based generalization error upper bound applicable to supervised learning scenarios.…

Information Theory · Computer Science 2021-01-11 Gholamali Aminian , Laura Toni , Miguel R. D. Rodrigues

In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…

Information Theory · Computer Science 2022-06-22 Tomer Berg , Or Ordentlich , Ofer Shayevitz

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Machine Learning · Statistics 2020-12-25 Yunbei Xu , Assaf Zeevi

Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…

Data Structures and Algorithms · Computer Science 2023-12-08 Nader H. Bshouty , Tsun-Ming Cheung , Gergely Harcos , Hamed Hatami , Anthony Ostuni

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…

Machine Learning · Statistics 2024-10-22 Chuhan Xie , Kaicheng Jin , Jiadong Liang , Zhihua Zhang

Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$…

Data Structures and Algorithms · Computer Science 2023-09-19 Nader H. Bshouty , Gergely Harcos

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Information Theory · Computer Science 2016-08-31 Jonathan Scarlett , Volkan Cevher

The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…

Quantum Physics · Physics 2014-12-23 Michael Walter , Joseph M. Renes

We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…

Computational Complexity · Computer Science 2026-05-12 Rishav Gupta , Bingkai Lin , Xin Zheng

We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…

Quantum Physics · Physics 2023-08-04 Andris Ambainis , Martins Kokainis , Jevgēnijs Vihrovs

We derive information-theoretic lower bounds on the Bayes risk and generalization error of realizable machine learning models. In particular, we employ an analysis in which the rate-distortion function of the model parameters bounds the…

Machine Learning · Computer Science 2021-11-09 Matthew Nokleby , Ahmad Beirami

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…

Applications · Statistics 2017-03-06 Arnab Koley , Debasis Kundu

In this paper, we study the sample complexity lower bounds for the exact recovery of parameters and for a positive excess risk of a feed-forward, fully-connected neural network for binary classification, using information-theoretic tools.…

Machine Learning · Statistics 2020-10-30 Xiaochen Yang , Jean Honorio

We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We…

Machine Learning · Computer Science 2024-10-28 Sam Lobel , Ronald Parr

We present a detailed study of estimation errors in terms of surrogate loss estimation errors. We refer to such guarantees as $\mathscr{H}$-consistency estimation error bounds, since they account for the hypothesis set $\mathscr{H}$…

Machine Learning · Computer Science 2022-05-18 Pranjal Awasthi , Anqi Mao , Mehryar Mohri , Yutao Zhong

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…

Information Theory · Computer Science 2016-07-05 Aolin Xu , Maxim Raginsky

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study…

Machine Learning · Computer Science 2021-01-26 Qinghua Liu , Zhou Lu

We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…

Statistics Theory · Mathematics 2014-03-06 Gabor Hannak , Alexander Jung , Norbert Goertz

We obtain a new lower bound on the information-based complexity of first-order minimization of smooth and convex functions. We show that the bound matches the worst-case performance of the recently introduced Optimized Gradient Method,…

Optimization and Control · Mathematics 2016-06-07 Yoel Drori