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A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

Discrete Mathematics · Computer Science 2017-09-28 Samantha Petti , Santosh Vempala

We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

Probability · Mathematics 2022-05-27 Xiao Fang , Yuta Koike

We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently…

Information Theory · Computer Science 2020-05-19 Jean Barbier , Galen Reeves

This article develops $p$-values for evaluating means of normal populations that make use of indirect or prior information. A $p$-value of this type is based on a biased test statistic that is optimal on average with respect to a…

Methodology · Statistics 2019-12-12 Peter D. Hoff

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…

Data Analysis, Statistics and Probability · Physics 2022-03-01 K. Gellerstedt , J. Sjölin

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

Statistics Theory · Mathematics 2025-02-24 Huiming Zhang , Song Xi Chen

In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional…

Probability · Mathematics 2007-05-23 Angelo Gilio

We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we…

Machine Learning · Computer Science 2018-11-19 Adarsh Barik , Jean Honorio , Mohit Tawarmalani

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Information Theory · Computer Science 2026-05-28 Yanxiao Liu , Yijun Fan , Deniz Gündüz

Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…

Methodology · Statistics 2015-01-20 Joe Whittaker , Florian Martin , Yang Xiang

In this paper, we develop local expansions for the ratio of the centered matrix-variate $T$ density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several…

Statistics Theory · Mathematics 2022-11-18 Frédéric Ouimet

We present a sparse representation of model uncertainty for Deep Neural Networks (DNNs) where the parameter posterior is approximated with an inverse formulation of the Multivariate Normal Distribution (MND), also known as the information…

Machine Learning · Computer Science 2020-06-23 Jongseok Lee , Matthias Humt , Jianxiang Feng , Rudolph Triebel

The newsvendor problem is a popular inventory management problem in supply chain management and logistics. Solutions to the newsvendor problem determine optimal inventory levels. This model is typically fully determined by a purchase and…

Applications · Statistics 2020-10-20 Sergey Tarima , Zhanna Zenkova

In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominently, Gaussian and Poisson models. More recent results due to Taborda and…

Information Theory · Computer Science 2012-08-01 Dongning Guo

Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, hence also confined to, several existing interpretations in various source coding problems. This…

Information Theory · Computer Science 2013-01-11 Ge Xu , Wei Liu , Biao Chen

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in a number of related literature.…

Machine Learning · Statistics 2020-01-31 Samuele Tosatto , Riad Akrour , Jan Peters

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…

Data Analysis, Statistics and Probability · Physics 2025-03-25 Jan Karbowski

In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities…

Machine Learning · Computer Science 2018-07-27 Moura Simon , Amini Massih-Reza , Louhichi Sana , Clausel Marianne

In his 2005 paper, S.T. Smith proposed an intrinsic Cram\'er-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a…

Systems and Control · Computer Science 2015-09-17 Silvère Bonnabel , Axel Barrau