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Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and…

Statistics Theory · Mathematics 2013-03-08 David Källberg , Oleg Seleznjev

This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust R\'enyi bounds, which provide LD estimates (and more…

Probability · Mathematics 2020-08-14 Rami Atar , Amarjit Budhiraja , Paul Dupuis , Ruoyu Wu

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets $X$ and $Y$, respectively with $N$ and $M$ samples, where $\eta:=M/N$…

Information Theory · Computer Science 2017-11-22 Morteza Noshad , Kevin R. Moon , Salimeh Yasaei Sekeh , Alfred O. Hero

This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…

Machine Learning · Computer Science 2012-05-14 Yishay Mansour , Mehryar Mohri , Afshin Rostamizadeh

We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…

Machine Learning · Statistics 2021-07-21 Jeremiah Birrell , Paul Dupuis , Markos A. Katsoulakis , Luc Rey-Bellet , Jie Wang

Differential Privacy (DP) is the leading approach to privacy preserving deep learning. As such, there are multiple efforts to provide drop-in integration of DP into popular frameworks. These efforts, which add noise to each gradient…

Machine Learning · Statistics 2021-06-08 Mathias Lécuyer

The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the…

Information Theory · Computer Science 2018-12-04 Lei Yu , Vincent Y. F. Tan

Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a combination of factors: computational advances making their optimization more tractable, their capacity to handle high dimensional problems, easy…

Numerical Analysis · Mathematics 2021-11-19 Akshunna S. Dogra

Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…

Quantum Physics · Physics 2024-08-23 Thomas A. Hahn , Ernest Y. -Z. Tan , Peter Brown

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new…

Statistics Theory · Mathematics 2020-08-18 Soumik Purkayastha , Ayanendranath Basu

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…

Machine Learning · Computer Science 2026-04-08 Shashaank Aiyer , Yishay Mansour , Shay Moran , Han Shao

Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its…

Portfolio Management · Quantitative Finance 2018-07-03 Nathan Lassance , Frédéric Vrins

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

Machine Learning · Computer Science 2024-01-17 Soyed Tuhin Ahmed

The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…

Information Theory · Computer Science 2018-09-19 Amos Lapidoth , Christoph Pfister

We evaluate the asymptotics of equivocations, their exponents as well as their second-order coding rates under various R\'{e}nyi information measures. Specifically, we consider the effect of applying a hash function on a source and we…

Information Theory · Computer Science 2016-07-06 Masahito Hayashi , Vincent Y. F. Tan

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…

Information Theory · Computer Science 2023-03-27 Amedeo Roberto Esposito , Adrien Vandenbroucque , Michael Gastpar

We propose a unified optimization framework for designing continuous and discrete noise distributions that ensure differential privacy (DP) by minimizing R\'enyi DP, a variant of DP, under a cost constraint. R\'enyi DP has the advantage…

Information Theory · Computer Science 2025-06-10 Atefeh Gilani , Juan Felipe Gomez , Shahab Asoodeh , Flavio P. Calmon , Oliver Kosut , Lalitha Sankar

Many differentially private (DP) data release systems either output DP synthetic data and leave analysts to perform inference as usual, which can lead to severe miscalibration, or output a DP point estimate without a principled way to do…

Machine Learning · Computer Science 2026-03-03 Amir Asiaee , Samhita Pal

This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…

Statistics Theory · Mathematics 2021-11-29 Sebastian Espinosa , Jorge F. Silva , Pablo Piantanida

Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…

Statistics Theory · Mathematics 2025-02-27 Alejandro Cholaquidis , Leonardo Moreno , Beatriz Pateiro-López