Bayesian Inference by Symbolic Model Checking

Salmani, Bahare; Katoen, Joost-Pieter

doi:10.1007/978-3-030-59854-9_9

Cited by 9 publications

(9 citation statements)

References 30 publications

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“…Related Work. The tight connection with inference has been recently investigated via the use of model checking for Bayesian networks, the prime model in probabilistic inference [56]. Bayesian networks can be described as probabilistic programs [10] and their operational semantics coincides with MCs [31].…”

Section: Discussion Related Work and Conclusionmentioning

confidence: 99%

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Holtzen

Junges

Vazquez-Chanlatte

et al. 2021

Computer Aided Verification

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We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool . Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio, with Rubicon as a first step towards integrating both perspectives.

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Section: Discussion Related Work and Conclusionmentioning

confidence: 99%

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Holtzen

Junges

Vazquez-Chanlatte

et al. 2021

Computer Aided Verification

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show abstract

“…Let M B = (Σ, σ I , P ) be the tree-like MC [41] of B. It is shown in [41], that inference on the BN B can be reduced to computing reachability probabilities on the tree-like MC M B , as…”

Section: A Some Detailed Experimental Resultsmentioning

confidence: 99%

“…A pBN2pMC transformation. This is inspired by our mapping of BNs onto treeshaped MCs [41] aimed at performing probabilistic inference using probabilistic model checking. Here, we propose an alternative transformation from (p)BNs into (p)MCs that yields more succinct (p)MCs, as it only keeps track of a subset of (p)BN variables at each "level" of the (p)MC.…”

Section: Analysing Parametric Bns Using Pmc Techniquesmentioning

confidence: 99%

Fine-Tuning the Odds in Bayesian Networks

Salmani¹,

Katoen²

2021

Preprint

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This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in parametric Markov chains. Our techniques are applicable to arbitrarily many, possibly dependent parameters that may occur in various CPTs. This lifts the severe restrictions on parameters, e.g., by restricting the number of parametrized CPTs to one or two, or by avoiding parameter dependencies between several CPTs, in existing works for parametric Bayes networks (pBNs). We describe how our techniques can be used for various pBN synthesis problems studied in the literature such as computing sensitivity functions (and values), simple and difference parameter tuning, ratio parameter tuning, and minimal change tuning. Experiments on several benchmarks show that our prototypical tool built on top of the probabilistic model checker Storm can handle several hundreds of parameters.

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“…[33]) and Bayesian networks (cf. [52]) with a large number of parameters. We took at least one variant of all POMDPs with reachability or expected reward properties from [8,47], except for the dining cryptographer's protocol which has a constant reachability probability.…”

Section: Set-upmentioning

confidence: 99%

Gradient-Descent for Randomized Controllers under Partial Observability

Heck¹,

Spel²,

Junges³

et al. 2021

Preprint

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Randomization is a powerful technique to create robust controllers, in particular in partially observable settings. The degrees of randomization have a significant impact on the system performance, yet they are intricate to get right. The use of synthesis algorithms for parametric Markov chains (pMCs) is a promising direction to support the design process of such controllers. This paper shows how to define and evaluate gradients of pMCs. Furthermore, it investigates varieties of gradient descent techniques from the machine learning community to synthesize the probabilities in a pMC. The resulting method scales to significantly larger pMCs than before and empirically outperforms the state-of-the-art, often by at least one order of magnitude.

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Bayesian Inference by Symbolic Model Checking

Cited by 9 publications

References 30 publications

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Fine-Tuning the Odds in Bayesian Networks

Gradient-Descent for Randomized Controllers under Partial Observability

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