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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,…

In this paper, we develop verifiable and computable performance analysis of sparsity recovery. We define a family of goodness measures for arbitrary sensing matrices as a set of optimization problems, and design algorithms with a…

Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…

Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…

Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function,…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…

In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…

We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…

In this paper, we address the approximate minimization problem of Markov Chains (MCs) from a behavioral metric-based perspective. Specifically, given a finite MC and a positive integer k, we are looking for an MC with at most k states…

Markov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not --…

We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

In this paper we develop a method to compute the solution to a countable (finite or infinite) set of equations that occurs in many different fields including Markov processes that model queueing systems, birth-and-death processes and…

We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates design and operational phases, which are represented by a mixed-integer program and discounted-cost…

We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…

A wide class of ``counting'' problems have been studied in Computer Science. Three typical examples are the estimation of - (i) the permanent of an $n\times n$ 0-1 matrix, (ii) the partition function of certain $n-$ particle Statistical…

We present an approach that can be useful when the network or system performance is described by a model that is not Markovian. Although most performance models are based on Markov chains or Markov processes, in some cases the Markov…