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A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

Statistics Theory · Mathematics 2008-12-18 Peter Radchenko

We introduce a family of information leakage measures called maximal $\alpha,\beta$-leakage, parameterized by real numbers $\alpha$ and $\beta$. The measure is formalized via an operational definition involving an adversary guessing an…

Information Theory · Computer Science 2022-11-29 Atefeh Gilani , Gowtham R. Kurri , Oliver Kosut , Lalitha Sankar

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

A conditional version of Sibson's $\alpha$-information is defined using a simple closed-form "log-expectation" expression, which satisfies important properties such as consistency, uniform expansion, and data processing inequalities. This…

Information Theory · Computer Science 2021-05-18 Yi Liu , Wei Cheng , Sylvain Guilley , Olivier Rioul

We consider the problem of quantifying the information shared by a pair of random variables $X_{1},X_{2}$ about another variable $S$. We propose a new measure of shared information, called extractable shared information, that is left…

Information Theory · Computer Science 2017-11-13 Johannes Rauh , Pradeep Kr. Banerjee , Eckehard Olbrich , Jürgen Jost , Nils Bertschinger

In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains…

Statistics Theory · Mathematics 2025-09-26 Bikramjit Das , Vicky Fasen-Hartmann

A common countermeasure against side-channel attacks on secret key cryptographic implementations is $d$th-order masking, which splits each sensitive variable into $d+1$ random shares. In this paper, maximal leakage bounds on the probability…

Information Theory · Computer Science 2023-05-11 Julien Béguinot , Yi Liu , Olivier Rioul , Wei Cheng , Sylvain Guilley

Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines,…

Computation · Statistics 2021-08-21 Luai Al-Labadi , Forough Fazeli-Asl , Zahra Saberi

We establish the Strong Poisson Hypothesis for symmetric closed networks. In particular, the asymptotic independence of the nodes -- as the size of the system tends to infinity -- is proved.

Probability · Mathematics 2016-10-27 Serge Pirogov , Alexander Rybko , Senya Shlosman , Alexander Vladimirov

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too…

Information Theory · Computer Science 2015-05-13 Tatsuto Murayama , Peter Davis

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…

Machine Learning · Computer Science 2021-03-04 Rishabh Iyer , Ninad Khargonkar , Jeff Bilmes , Himanshu Asnani

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…

Probability · Mathematics 2007-05-23 Ph . Barbe , W. P. McCormick , C. Zhang

The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic…

Signal Processing · Electrical Eng. & Systems 2022-06-22 Yijun Ding , Amit Ashok

For $\tilde{f}(t) = \exp(\frac{\alpha-1}{\alpha}t)$, this paper shows that the Sibson mutual information is an $\alpha$-leakage averaged over the adversary's $\tilde{f}$-mean relative information gain (on the secret) at elementary event of…

Information Theory · Computer Science 2025-10-09 Ni Ding , Farhad Farokhi , Tao Guo , Yinfei Xu , Xiang Zhang

In this work, maximal $\alpha$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an…

Quantum Physics · Physics 2024-03-22 Bo-Yu Yang , Hsuan Yu , Hao-Chung Cheng

Does the asymptotic variance of the maximum composite likelihood estimator of a parameter of interest always decrease when the nuisance parameters are known? Will a composite likelihood necessarily become more efficient by incorporating…

Statistics Theory · Mathematics 2016-12-22 Ximing Xu , Nancy Reid , Libai Xu

Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…

Statistics Theory · Mathematics 2025-09-17 Marta Catalano , Hugo Lavenant

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…

Information Theory · Computer Science 2020-07-15 Lampros Gavalakis , Ioannis Kontoyiannis

In this paper we improve the probabilistic approach to compositions of Ehrenborg, Levin and Readdy by introducing a simpler but more general probabilistic model. As consequence we get some new estimates on the behavior of a uniform random…

Probability · Mathematics 2015-01-28 Pierre Tarrago

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