Related papers: Accelerating Parametric Probabilistic Verification
Quantum walks on graphs have been shown in certain cases to mix quadratically faster than their classical counterparts. Lifted Markov chains, consisting of a Markov chain on an extended state space which is projected back down to the…
We introduce a framework to approximate a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…
We introduce the problem of formally verifying properties of Markov processes where the parameters are given by the output of machine learning models. For a broad class of machine learning models, including linear models, tree-based models,…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac…
Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an…
We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…
We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on…
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…
In this study, we address the central issue of statistical inference for Markov jump processes using discrete time observations. The primary problem at hand is to accurately estimate the infinitesimal generator of a Markov jump process, a…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…