Related papers: Divergence Inequalities with Applications in Ergod…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversible case, weak convergence rates of the transition kernels…
An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an…
Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…
In two phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
We derive uniform concentration inequalities for continuous-time analogues of empirical processes and related stochastic integrals of scalar ergodic diffusion processes. Thereby, we lay the foundation typically required for the study of…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
Explicit rate of convergence in variance (or more general entropies) is obtained for a class of Piecewise Deterministic Markov Processes such as the TCP process, relying on functional inequalities. A method to establish Poincar\'e (and more…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…
We consider fair resource allocation in sequential decision-making environments modeled as weakly coupled Markov decision processes, where resource constraints couple the action spaces of $N$ sub-Markov decision processes (sub-MDPs) that…
Functional inequalities such as the Poincar\'e and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications,…
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…