Related papers: Various Ways to Quantify BDMPs

Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…

We propose deterministic timed automata (DTA) as a model-independent language for specifying performance and dependability measures over continuous-time stochastic processes. Technically, these measures are defined as limit frequencies of…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

Stochastic gene regulatory networks with bursting dynamics can be modeled mesocopically as a generalized density-dependent Markov chain (GDDMC) or macroscopically as a piecewise-deterministic Markov process (PDMP). Here we prove a limit…

Concept Bottleneck Models (CBMs) enhance interpretability by introducing a layer of human-understandable concepts between inputs and predictions. While recent methods automate concept generation using Large Language Models (LLMs) and…

In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…

Linear multistep methods (LMMs) applied to approximate the solution of initial value problems---typically arising from method-of-lines semidiscretizations of partial differential equations---are often required to have certain monotonicity…

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits…

Controlling stochastic systems with unknown dynamics and under complex specifications is specially challenging in safety-critical settings, where performance guarantees are essential. We propose a data-driven policy synthesis framework that…

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control…

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…

Markov Chain Monte Carlo (MCMC) techniques have long been studied in computational geometry subjects whereabouts the problems to be studied are complex geometric objects which by their nature require optimized techniques to be deployed or…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

Bounded model checking (BMC) is an efficient formal verification technique which allows for desired properties of a software system to be checked on bounded runs of an abstract model of the system. The properties are frequently described in…

Deep learning representations are often difficult to interpret, which can hinder their deployment in sensitive applications. Concept Bottleneck Models (CBMs) have emerged as a promising approach to mitigate this issue by learning…

Causal learning tackles the computationally demanding task of estimating causal graphs. This paper introduces a new divide-and-conquer approach for causal graph learning, called DCILP. In the divide phase, the Markov blanket MB($X_i$) of…

This work provides test error bounds for iterative fixed point methods on linear predictors -- specifically, stochastic and batch mirror descent (MD), and stochastic temporal difference learning (TD) -- with two core contributions: (a) a…

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…

The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed…

Stochastic model checking is a technique for analyzing systems that possess probabilistic characteristics. However, its scalability is limited as probabilistic models of real-world applications typically have very large or infinite state…