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Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model…

Machine Learning · Statistics 2025-11-06 Jean Pacifique Nkurunziza , Fulgence Nahayo , Nicolas Gillis

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we…

Physics and Society · Physics 2016-12-23 Manlio De Domenico , Jacob Biamonte

We consider estimating the predictive density under Kullback-Leibler loss in a high-dimensional Gaussian model. Decision theoretic properties of the within-family prediction error -- the minimal risk among estimates in the class…

Statistics Theory · Mathematics 2012-12-04 Gourab Mukherjee , Iain M. Johnstone

The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…

Machine Learning · Computer Science 2025-07-31 Adwait Datar , Nihat Ay

Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These…

Statistics Theory · Mathematics 2019-07-02 Alexander Bulinski , Denis Dimitrov

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…

Methodology · Statistics 2018-02-19 Yilei Wu , Yingli Qin , Mu Zhu

One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…

Computation · Statistics 2017-07-28 Tomer Lancewicki

Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and…

Machine Learning · Computer Science 2023-03-13 Jonas Wildberger , Siyuan Guo , Arnab Bhattacharyya , Bernhard Schölkopf

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…

Methodology · Statistics 2016-05-17 T. Tony Cai , Anru Zhang

We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…

Statistics Theory · Mathematics 2017-01-19 Arnak S. Dalalyan , Mehdi Sebbar

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Methodology · Statistics 2025-12-30 Shaoxin Wang , Ziyun Ma

We consider the problem of estimating the covariance matrix of a random vector by observing i.i.d samples and each entry of the sampled vector is missed with probability $p$. Under the standard $L_4-L_2$ moment equivalence assumption, we…

Statistics Theory · Mathematics 2024-06-17 Pedro Abdalla

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the "classical" case of…

Computation · Statistics 2015-08-04 Holger Dette , Roman Guchenko , Viatcheslav B. Melas

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Statistics Theory · Mathematics 2015-03-19 Michel Broniatowski , Aida Toma , Igor Vajda

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

Machine Learning · Computer Science 2025-08-25 Sebastian Sanokowski , Sepp Hochreiter , Sebastian Lehner

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Statistics Theory · Mathematics 2014-12-20 Jean Lafond , Olga Klopp , Eric Moulines , Jospeh Salmon

Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a…

Methodology · Statistics 2008-11-04 Astrid Jourdan

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

Machine Learning · Computer Science 2019-06-12 Yu Cheng , Ilias Diakonikolas , Rong Ge , David Woodruff

Experimental designs are tools which can drastically reduce the number of simulations required by time-consuming computer codes. One strategy for selecting the values of the inputs, whose response is to be observed, is to choose these…

Statistics Theory · Mathematics 2009-04-17 Astrid Jourdan , Jessica Franco

Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…

Information Theory · Computer Science 2020-02-27 Puning Zhao , Lifeng Lai