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In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Arjun K. Gupta , Nestor Parolya

We study the problem of selecting optimal two-block partitions to accelerate the mixing of finite Markov chains under group-averaging transformations. The main objectives considered are the Kullback-Leibler (KL) divergence and the Frobenius…

Probability · Mathematics 2026-03-12 Ryan J. Y. Lim , Michael C. H. Choi

The Kullback-Leibler divergence offers an information-theoretic basis for measuring the difference between two given distributions. Its quantum analog, however, fails to play a corresponding role for comparing two density matrices, if the…

Quantum Physics · Physics 2009-11-10 Sumiyoshi Abe

The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…

Signal Processing · Electrical Eng. & Systems 2025-11-05 Marios Impraimakis

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…

Statistics Theory · Mathematics 2012-05-14 Karim Lounici

Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…

Statistics Theory · Mathematics 2023-11-13 Karim Lounici , Grégoire Pacreau

Estimating the Kullback-Leibler (KL) divergence between random variables is a fundamental problem in statistical analysis. For continuous random variables, traditional information-theoretic estimators scale poorly with dimension and/or…

Machine Learning · Computer Science 2025-10-08 Mikil Foss , Andrew Lamperski

Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The…

Machine Learning · Computer Science 2019-08-20 Kartik Ahuja

Meta-analytic methods tend to take all-or-nothing approaches to study-level heterogeneity, assuming all studies are heterogeneous or homogeneous, leading to inefficiency and/or bias in estimation and inference. In this paper, we develop a…

Methodology · Statistics 2026-03-12 Elizabeth M. Davis , Emily C. Hector

In traditional Machine Learning, the algorithms predictions are based on the assumption that the data follows the same distribution in both the training and the test datasets. However, in real world data this condition does not hold and,…

Machine Learning · Computer Science 2024-02-05 Laura Fdez-Díaz , Sara González Tomillo , Elena Montañés , José Ramón Quevedo

In this paper, we compare the performance of two methods for estimating Bayesian networks from data containing exogenous variables and random effects. The first method is fully Bayesian in which a prior distribution is placed on the…

Methodology · Statistics 2011-12-02 Jessica Kasza , Patty Solomon

Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…

Signal Processing · Electrical Eng. & Systems 2026-01-05 Jeongwoo Park , Seongkyu Jung , Kaiming Shen , Jeonghun Park

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

Statistics Theory · Mathematics 2010-03-04 Sanjay Chaudhuri , Mathias Drton , Thomas S. Richardson

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

Methodology · Statistics 2022-04-20 Yichi Zhang , Weining Shen , Dehan Kong

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Statistics Theory · Mathematics 2024-04-03 Jinyuan Chang , Qiao Hu , Cheng Liu , Cheng Yong Tang

We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy…

Medical Physics · Physics 2021-07-14 Wooseok Ha , Emil Y. Sidky , Rina Foygel Barber , Taly Gilat Schmidt , Xiaochuan Pan

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

Statistics Theory · Mathematics 2026-04-09 Giuseppe Carere , Han Cheng Lie

For the multivariate linear regression model with unknown covariance, the corrected Akaike information criterion is the minimum variance unbiased estimator of the expected Kullback--Leibler discrepancy. In this study, based on the loss…

Statistics Theory · Mathematics 2023-03-20 Takeru Matsuda

Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…

Machine Learning · Statistics 2022-07-28 Mingxuan Yi , Song Liu

We consider the problem of quantifying the quality of a model selection problem for a graphical model. We discuss this by formulating the problem as a detection problem. Model selection problems usually minimize a distance between the…

Information Theory · Computer Science 2017-10-19 Navid Tafaghodi Khajavi , Anthony Kuh