Fine-Tuning the Odds in Bayesian Networks

Salmani, Bahare; Katoen, Joost-Pieter

doi:10.1007/978-3-030-86772-0_20

Cited by 6 publications

(5 citation statements)

References 44 publications

(14 reference statements)

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“…Beyond Markov models, probabilistic graphical models in general and Bayesian networks in particular are widespread to describe complex conditional probability distributions. Recent work [72,73] shows that ideas and methods for parameter synthesis in Markov chains as described in this survey significantly improve upon existing methods for parametric Bayesian networks [21]. Vice versa, some inference techniques do yield interesting alternatives for the analysis of (finite-horizon properties in) pMCs [46].…”

Section: Epiloguementioning

confidence: 95%

“…For most cases, state elimination (significantly) outperforms Gaussian elimination. Recent experiments [72] indicate that the techniques described above significantly outperform similar techniques used for probabilistic graphical models; e.g., for Bayesian network win95pts 5 with 76 random variable and 200 parameters spread randomly over the graph, the solution function with about 7,5 million monomials of maximal degree 16 could be computed in about 400 s. It is also beneficial to compute solution functions in a compositional way rather than on a monolithic pMC. This has been advocated for each strongly connected component separately [49] and more recently for more liberal decompositions of the graphical structure of the pMC [35].…”

Section: Exact Partitioningmentioning

confidence: 99%

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Parameter Synthesis in Markov Models: A Gentle Survey

Jansen¹,

Junges²,

Katoen³

2022

Lecture Notes in Computer Science

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This paper surveys the analysis of parametric Markov models whose transitions are labelled with functions over a finite set of parameters. These models are symbolic representations of uncountable many concrete probabilistic models, each obtained by instantiating the parameters. We consider various analysis problems for a given logical specification ϕ: do all parameter instantiations within a given region of parameter values satisfy ϕ?, which instantiations satisfy ϕ and which ones do not?, and how can all such instantiations be characterised, either exactly or approximately? We address theoretical complexity results and describe the main ideas underlying state-of-the-art algorithms that established an impressive leap over the last decade enabling the fully automated analysis of models with millions of states and thousands of parameters.

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Section: Epiloguementioning

confidence: 95%

Section: Exact Partitioningmentioning

confidence: 99%

Parameter Synthesis in Markov Models: A Gentle Survey

Jansen¹,

Junges²,

Katoen³

2022

Lecture Notes in Computer Science

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“…For acyclic DTMCs the EVT of a state coincides with the probability of reaching this state. This is relevant in the context of Bayesian networks [53,54] since inference queries in the network can be reduced to reachability queries by translating Bayesian networks into tree-like DTMCs. Existing procedures for multi-objective model checking of MDPs employ linear programming methods relying on the EVTs of state-action pairs [20,18,13,17].…”

Section: Related Workmentioning

confidence: 99%

Accurately Computing Expected Visiting Times and Stationary Distributions in Markov Chains

Mertens,

Katoen,

Quatmann

et al. 2024

Lecture Notes in Computer Science

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We study the accurate and efficient computation of the expected number of times each state is visited in discrete- and continuous-time Markov chains. To obtain sound accuracy guarantees efficiently, we lift interval iteration and topological approaches known from the computation of reachability probabilities and expected rewards. We further study applications of expected visiting times, including the sound computation of the stationary distribution and expected rewards conditioned on reaching multiple goal states. The implementation of our methods in the probabilistic model checker scales to large systems with millions of states. Our experiments on the quantitative verification benchmark set show that the computation of stationary distributions via expected visiting times consistently outperforms existing approaches — sometimes by several orders of magnitude.

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“…The methods presented in [13,22] exploit a repetitive structure in parametric MCs to accelerate the construction of closed form solutions and are not applicable to MDPs. Parametric models have been used to support the design of systems [2,8] or their adaption [6,9], to find policies for partially observable systems [11], to analyse Bayesian networks [34], and to speed up the analysis of, e.g., software product lines [10,37]. On top of technical differences, none of these approaches uses a hierarchical decomposition of an MDP or uses the results of the analysis in the analysis of a larger MDP.…”

Section: Related Workmentioning

confidence: 99%

Abstraction-Refinement for Hierarchical Probabilistic Models

Junges

Spaan

2022

Computer Aided Verification

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Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by exploiting a hierarchical structure with repetitive parts. This structure not only occurs naturally in robotics, but also in probabilistic programs describing, e.g., network protocols. Such programs often repeatedly call a subroutine with similar behavior. In this paper, we focus on a local case, in which the subroutines have a limited effect on the overall system state. The key ideas to accelerate analysis of such programs are (1) to treat the behavior of the subroutine as uncertain and only remove this uncertainty by a detailed analysis if needed, and (2) to abstract similar subroutines into a parametric template, and then analyse this template. These two ideas are embedded into an abstraction-refinement loop that analyses hierarchical MDPs. A prototypical implementation shows the efficacy of the approach.

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Fine-Tuning the Odds in Bayesian Networks

Cited by 6 publications

References 44 publications

Parameter Synthesis in Markov Models: A Gentle Survey

Parameter Synthesis in Markov Models: A Gentle Survey

Accurately Computing Expected Visiting Times and Stationary Distributions in Markov Chains

Abstraction-Refinement for Hierarchical Probabilistic Models

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