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Related papers: Scenario Approach for Parametric Markov Models

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We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…

Formal Languages and Automata Theory · Computer Science 2021-10-04 Stefan Kiefer , Qiyi Tang

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…

Machine Learning · Computer Science 2024-02-07 Shivvrat Arya , Tahrima Rahman , Vibhav Gogate

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best…

Data Structures and Algorithms · Computer Science 2020-11-06 Nima Anari , Moses Charikar , Kirankumar Shiragur , Aaron Sidford

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…

Computation · Statistics 2017-01-02 Arthur Szlam , Yuval Kluger , Mark Tygert

This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Keerthi Chacko , Midhun T. Augustine , S. Janardhanan , Deepak U. Patil , I. N. Kar

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…

Logic in Computer Science · Computer Science 2018-06-14 Sebastian Arming , Ezio Bartocci , Krishnendu Chatterjee , Joost-Pieter Katoen , Ana Sokolova

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

Probability · Mathematics 2014-03-10 Christophe Andrieu , Matti Vihola

Design and control of autonomous systems that operate in uncertain or adversarial environments can be facilitated by formal modelling and analysis. Probabilistic model checking is a technique to automatically verify, for a given temporal…

Logic in Computer Science · Computer Science 2021-11-23 Marta Kwiatkowska , Gethin Norman , David Parker

We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…

Numerical Analysis · Mathematics 2017-04-04 Markus Bachmayr , Albert Cohen , Wolfgang Dahmen

We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…

Logic in Computer Science · Computer Science 2022-12-08 Thom S. Badings , Nils Jansen , Sebastian Junges , Marielle Stoelinga , Matthias Volk

Markov decision processes are useful models of concurrency optimisation problems, but are often intractable for exhaustive verification methods. Recent work has introduced lightweight approximative techniques that sample directly from…

Logic in Computer Science · Computer Science 2015-03-24 Axel Legay , Sean Sedwards , Louis-Marie Traonouez

In this paper, we consider approximations of principal component projection (PCP) without explicitly computing principal components. This problem has been studied in several recent works. The main feature of existing approaches is viewing…

Numerical Analysis · Mathematics 2019-02-26 Stephen D. Farnham , Lixin Shen , Bruce W. Suter

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…

Machine Learning · Computer Science 2023-05-03 Thom Badings , Sebastian Junges , Ahmadreza Marandi , Ufuk Topcu , Nils Jansen

The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…

Optimization and Control · Mathematics 2022-01-04 Warren B Powell , Saeed Ghadimi

We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…

Logic in Computer Science · Computer Science 2016-03-04 Przemysław Daca , Thomas A. Henzinger , Jan Křetínský , Tatjana Petrov

The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…

Information Theory · Computer Science 2018-04-04 Ulan N. Brimkulov , Chinara Jumabaeva , Kasym Baryktabasov

We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms…

Data Structures and Algorithms · Computer Science 2017-12-20 Jaroslaw Byrka , Aravind Srinivasan

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…

Numerical Analysis · Mathematics 2017-04-06 Silvia Noschese , Lothar Reichel

We employ the scenario approach to compute probably approximately correct (PAC) bounds on the average inter-sample time (AIST) generated by an unknown PETC system, based on a finite number of samples. We extend the scenario approach to…

Systems and Control · Electrical Eng. & Systems 2022-03-11 Andrea Peruffo , Manuel Mazo

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are…

Machine Learning · Computer Science 2023-09-20 Noah Golowich , Ankur Moitra , Dhruv Rohatgi