Related papers: A Spectrum of Approximate Probabilistic Bisimulati…

This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…

We extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define…

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A…

Bayesian inference for Continuous-Time Markov Chains (CTMCs) on countably infinite spaces is notoriously difficult because evaluating the likelihood exactly is intractable. One way to address this challenge is to first build a non-negative…

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on $\mathbb R^d$. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel…

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of…

Consider a Markov chain defined on a finite state space, X, that leaves invariant the uniform distribution on X, and whose transition probabilities are integer multiples of 1/Q, for some integer Q. I show how a simulation of n transitions…

Probabilistic inference provides a language for describing how organisms may learn from and adapt to their environment. The computations needed to implement probabilistic inference often require specific representations, akin to having the…

Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…

In this paper we study strong and weak bisimulation equivalences for continuous-time Markov decision processes (CTMDPs) and the logical characterizations of these relations with respect to the continuous-time stochastic logic (CSL). For…

We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.

This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…

Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…

We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…

Probabilistic Logic Programming (PLP) languages enable programmers to specify systems that combine logical models with statistical knowledge. The inference problem, to determine the probability of query answers in PLP, is intractable in…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…