6 papers
Minimax Quantile Bounds via Information Measures
Amedeo Roberto Esposito
We develop a unified information-theoretic framework for lower bounding minimax quantiles. The starting point is a loss-adapted Neyman--Pearson metaconverse that bounds the minimax…
A Finite-Sample Strong Converse for Binary Hypothesis Testing via (Reverse) Rényi Divergence
Roberto Bruno, Adrien Vandenbroucque, Amedeo Roberto Esposito
This work investigates binary hypothesis testing between and in the finite-sample regime under asymmetric error constraints. By employing the ``reverse"…
Contraction of Rényi Divergences for Discrete Channels: Properties and Applications
Adrien Vandenbroucque, Amedeo Roberto Esposito, Michael Gastpar
This work explores properties of Strong Data-Processing constants for Rényi Divergences. Parallels are made with the well-studied -Divergences, and it is shown that the order…
Contraction of Markovian Operators in Orlicz Spaces and Error Bounds for Markov Chain Monte Carlo
Amedeo Roberto Esposito, Marco Mondelli
We introduce a novel concept of convergence for Markovian processes within Orlicz spaces, extending beyond the conventional approach associated with spaces. After showing tha…
Geometric Convergence Analysis of Variational Inference via Bregman Divergences
Sushil Bohara, Amedeo Roberto Esposito
Variational Inference (VI) provides a scalable framework for Bayesian inference by optimizing the Evidence Lower Bound (ELBO), but convergence analysis remains challenging due to t…
Sibson -Mutual Information and Its Variational Representations
Amedeo Roberto Esposito, Michael Gastpar, Ibrahim Issa
Information measures can be constructed from Rényi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson -mu…