Related papers: Hoeffding's Inequality for Markov Chains under Gen…
Training modern neural networks often relies on large learning rates, operating at the edge of stability, where the optimization dynamics exhibit oscillatory and chaotic behavior. Empirically, this regime often yields improved…
In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of…
State aggregation aims to reduce the computational complexity of solving Markov Decision Processes (MDPs) while preserving the performance of the original system. A fundamental challenge lies in optimizing policies within the aggregated, or…
Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
We investigate the application of Weak Poincar\'e Inequalities (WPI) to Markov chains to study their rates of convergence and to derive complexity bounds. At a theoretical level we investigate the necessity of the existence of WPIs to…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…
Suitable reachability conditions can make two different fixed point semantics of a transition system coincide. For instance, the total and partial expected reward semantics on Markov chains (MCs) coincide whenever the MC at hand is almost…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher…
We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…