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The $\alpha$-divergences include the well-known Kullback-Leibler divergence, Hellinger distance and $\chi^2$-divergence. In this paper, we derive differential and integral relations between the $\alpha$-divergences that are generalizations…

Information Theory · Computer Science 2022-11-29 Tomohiro Nishiyama

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values…

Information Theory · Computer Science 2009-06-09 Mark D. Reid , Robert C. Williamson

We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in…

Probability · Mathematics 2017-11-29 Apoorva Khare , Bala Rajaratnam

Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…

Information Theory · Computer Science 2025-07-14 Amedeo Roberto Esposito , Michael Gastpar , Ibrahim Issa

This work presents an infinite-dimensional generalization of the correspondence between the Kullback-Leibler and R\'enyi divergences between Gaussian measures on Euclidean space and the Alpha Log-Determinant divergences between symmetric,…

Probability · Mathematics 2019-04-12 Minh Ha Quang

Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the…

Methodology · Statistics 2018-10-09 Tomohiro Nishiyama

The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric…

Statistics Theory · Mathematics 2026-01-27 Tetsuya Kaji

Many evaluation measures are used to evaluate social biases in masked language models (MLMs). However, we find that these previously proposed evaluation measures are lacking robustness in scenarios with limited datasets. This is because…

Computation and Language · Computer Science 2024-01-23 Yang Liu

Automated feature selection is important for text categorization to reduce the feature size and to speed up the learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the…

Machine Learning · Statistics 2016-11-15 Bo Tang , Steven Kay , Haibo He

The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between…

Machine Learning · Statistics 2026-03-03 Shiji Xiao , Yufeng Zhang , Chubo Liu , Yan Ding , Keqin Li , Kenli Li

We generalize the family of $\alpha$-divergences using a pair of strictly comparable weighted means. In particular, we obtain the $1$-divergence in the limit case $\alpha\rightarrow 1$ (a generalization of the Kullback-Leibler divergence)…

Information Theory · Computer Science 2022-11-23 Frank Nielsen

The concept of varentropy has been recently introduced as a dispersion index of the reliability of measure of information. In this paper, we introduce new measures of variability for two measures of uncertainty, the Kerridge inaccuracy…

Probability · Mathematics 2021-12-16 Francesco Buono , Camilla Calì , Maria Longobardi

To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined…

Machine Learning · Computer Science 2018-04-05 Boris Belousov , Jan Peters

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

Information Theory · Computer Science 2020-01-03 Amichai Painsky , Gregory W. Wornell

Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…

Statistics Theory · Mathematics 2022-03-30 Sreejith Sreekumar , Ziv Goldfeld

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

Statistics Theory · Mathematics 2021-06-08 Rohit Agrawal , Thibaut Horel

Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be performed using the celebrated $k$-means centroid-based…

Information Theory · Computer Science 2014-01-23 Frank Nielsen

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…

Information Theory · Computer Science 2016-11-17 Igal Sason

We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root of these divergences is a distance metric. As a corollary we obtain a proof of the metric property for…

Information Theory · Computer Science 2019-12-17 Suvrit Sra

Analyzing correlation between variables is often both the tool and the goal of modern science. A crucial question is whether the correlation between two variables is a direct correlation or only an indirect correlation through a confounder.…

Methodology · Statistics 2026-04-22 Shengjun Wu , Jeffery Wu