Publications related to Hellinger distance

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results i ...

2022

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Michael Christoph Gastpar, Adriano Pastore

We consider a setup in which confidential i.i.d. samples X1, . . . , Xn from an unknown finite-support distribution p are passed through n copies of a discrete privatization chan- nel (a.k.a. mechanism) producing outputs Y1, . . . , Yn. The channel law gua ...

2021

Robust Generalization via f−Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

Given two probability measures P and Q and an event E, we provide bounds on P(E) in terms of Q(E) and f-divergences. In particular, the bounds are instantiated when the measures considered are a joint distribution and the corresponding product of marginals ...

IEEE2020

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

Double-Loop Unadjusted Langevin Algorithm

Volkan Cevher, Paul Thierry Yves Rolland, Ali Kavis, Armin Eftekhari

A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling ...

2020

Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Serge Vaudenay

The maximal achievable advantage of a (computationally unbounded) distinguisher to determine whether a source

Z

is distributed according to distribution

P_0

P_1

, when given access to one sample of

Z

, is characterized by the statistical distance ...

Springer, Cham2020

Study of constrained Brownian motion of nanoparticles near an interface using optical tweezers

Martinus Gijs, Thomas Lehnert, Matteo Cornaglia, Raphaël Etienne Jean Trouillon, Hui Yang

We demonstrate a method to determine the Brownian motion and the diffusion coefficient of a nanoparticle in water in a plane that is parallel to a solid boundary and as function of the distance normal to that boundary by using an optical tweezers instrumen ...

Spie-Int Soc Optical Engineering2015

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Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Serge Vaudenay

The maximal achievable advantage of a (computationally unbounded) distinguisher to determine whether a source

Z

is distributed according to distribution

P_0

P_1

, when given access to one sample of

Z

, is characterized by the statistical distance ...

Springer, Cham2020

Hellinger distance

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Robust Generalization via f−Mutual Information

Strong convergence of multivariate maxima

Double-Loop Unadjusted Langevin Algorithm

Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Improving the arm-hand coordination in neuroprosthetics control with prior information from muscle activity

Unsupervised Learning of Representations for Lexical Entailment Detection

Study of constrained Brownian motion of nanoparticles near an interface using optical tweezers

Graph Chatbot

Chat with Graph Search

Improving the arm-hand coordination in neuroprosthetics control with prior information from muscle activity

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Unsupervised Learning of Representations for Lexical Entailment Detection

Robust Generalization via f−Mutual Information

Double-Loop Unadjusted Langevin Algorithm

Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Study of constrained Brownian motion of nanoparticles near an interface using optical tweezers

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Strong convergence of multivariate maxima