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$\alpha$-posteriors and their variational approximations distort standard posterior inference by downweighting the likelihood and introducing variational approximation errors. We show that such distortions, if tuned appropriately, reduce…

Machine Learning · Statistics 2021-04-20 Marco Avella Medina , José Luis Montiel Olea , Cynthia Rush , Amilcar Velez

In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of 1) a weighted Mean Square Error (wMSE)…

Computer Vision and Pattern Recognition · Computer Science 2024-10-29 Jiequan Cui , Zhuotao Tian , Zhisheng Zhong , Xiaojuan Qi , Bei Yu , Hanwang Zhang

We derive the Kullback-Leibler divergence for the normal-gamma distribution and show that it is identical to the Bayesian complexity penalty for the univariate general linear model with conjugate priors. Based on this finding, we provide…

Statistics Theory · Mathematics 2016-11-07 Joram Soch , Carsten Allefeld

We study the problem of characterizing the stability of Kullback-Leibler (KL) divergence under Gaussian perturbations beyond Gaussian families. Existing relaxed triangle inequalities for KL divergence critically rely on the assumption that…

Machine Learning · Computer Science 2026-04-17 Jialu Pan , Yufeng Zhang , Nan Hu , Zhenbang Chen , Ji Wang , Keqin Li

Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic…

Statistics Theory · Mathematics 2024-12-25 Jason M. Altschuler , Sinho Chewi

In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of (1) a weighted Mean Square Error (wMSE)…

Machine Learning · Computer Science 2025-03-12 Jiequan Cui , Beier Zhu , Qingshan Xu , Zhuotao Tian , Xiaojuan Qi , Bei Yu , Hanwang Zhang , Richang Hong

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…

Optimization and Control · Mathematics 2017-11-22 San Gultekin , John Paisley

Domain adaptation is an important problem and often needed for real-world applications. In this problem, instead of i.i.d. training and testing datapoints, we assume that the source (training) data and the target (testing) data have…

Machine Learning · Computer Science 2022-03-15 A. Tuan Nguyen , Toan Tran , Yarin Gal , Philip H. S. Torr , Atılım Güneş Baydin

We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…

Information Theory · Computer Science 2019-10-22 Jay Mardia , Jiantao Jiao , Ervin Tánczos , Robert D. Nowak , Tsachy Weissman

The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…

Other Computer Science · Computer Science 2025-05-06 William Cook

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with…

Machine Learning · Statistics 2018-01-09 Robert Bamler , Cheng Zhang , Manfred Opper , Stephan Mandt

The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is…

Information Theory · Computer Science 2018-02-22 Yuheng Bu , Shaofeng Zou , Yingbin Liang , Venugopal V. Veeravalli

This short note is on a property of the Kullback-Leibler (KL) divergence which indicates that independent Gaussian distributions minimize the KL divergence from given independent Gaussian distributions. The primary purpose of this note is…

Information Theory · Computer Science 2020-12-04 Song Fang , Quanyan Zhu

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

The deepening penetration of renewable resources into power systems entails great difficulties that have not been surmounted satisfactorily. An issue that merits special attention is the short-term planning of power systems under net load…

Optimization and Control · Mathematics 2020-12-15 Ogun Yurdakul , Fikret Sivrikaya , Sahin Albayrak

A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…

Mathematical Physics · Physics 2019-06-11 Domenico Felice , Stefano Mancini , Nihat Ay

We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…

Information Theory · Computer Science 2021-01-05 Yan Wang

Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…

Information Theory · Computer Science 2017-03-30 David J. Galas , T. Gregory Dewey , James Kunert-Graf , Nikita A. Sakhanenko

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…

Methodology · Statistics 2018-05-21 Papa Ngom , Freedath Djibril Moussa , Jean de Dieu Nkurunziza

We propose a Kullback-Leibler Divergence (KLD) filter to extract anomalies within data series generated by a broad class of proximity sensors, along with the anomaly locations and their relative sizes. The technique applies to devices…

Signal Processing · Electrical Eng. & Systems 2024-05-07 Ruikun Zhou , Wail Gueaieb , Davide Spinello