Perturbation analysis of stochastic systems with empirical distribution parameters

Su, Guoxin; Rosenblum, David S.

doi:10.1145/2568225.2568256

Cited by 11 publications

(16 citation statements)

References 31 publications

(23 reference statements)

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“…In particular, we show how to compute the linear and the quadratic asymptotic bounds. This subsumes the resuls reported previously [31] regarding linear asymptotic bounds. The computation of non-asymptotic bounds is related to verification of stochastic models with uncertainty (e.g.…”

Section: If Some Of the Quantities In The Stochastic Model Are Pertursupporting

confidence: 91%

“…These norms are widely adopted in literature (e.g. [8,15,31]), and somehow are easy to compute as they are "linear". Henceforth, we refer to the three distances as Type I, II and III distances, respectively.…”

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

“…The study of asymptotic bounds in probabilistic verification was initiated by Su et al [30,31], where linear and quadratic asymptotic bounds with respect to a single perturbation distance function are studied. Apart from giving a unified formulation of general asymptotic bounds under the three types of distances, the current paper also improves the complexity results reported in the previous work.…”

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

“…However, the presented techniques can be generalised for ω-regular properties and various performance properties, such as expected rewards and long-run average rewards, without substantial difficulty (and see our previous work [31] for ω-regular properties).…”

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

See 3 more Smart Citations

Perturbation Analysis in Verification of Discrete-Time Markov Chains

Chen¹,

Feng

Rosenblum

et al. 2014

CONCUR 2014 – Concurrency Theory

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Abstract. Perturbation analysis in probabilistic verification addresses the robustness and sensitivity problem for verification of stochastic models against qualitative and quantitative properties. We identify two types of perturbation bounds, namely non-asymptotic bounds and asymptotic bounds. Non-asymptotic bounds are exact, pointwise bounds that quantify the upper and lower bounds of the verification result subject to a given perturbation of the model, whereas asymptotic bounds are closed-form bounds that approximate non-asymptotic bounds by assuming that the given perturbation is sufficiently small. We perform perturbation analysis in the setting of Discrete-time Markov Chains. We consider three basic matrix norms to capture the perturbation distance, and focus on the computational aspect. Our main contributions include algorithms and tight complexity bounds for calculating both non-asymptotic bounds and asymptotic bounds with respect to the three perturbation distances.

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Section: If Some Of the Quantities In The Stochastic Model Are Pertursupporting

confidence: 91%

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

Section: If Some Of the Quantities In The Stochastic Model Are Perturmentioning

confidence: 99%

See 2 more Smart Citations

Perturbation Analysis in Verification of Discrete-Time Markov Chains

Chen¹,

Feng

Rosenblum

et al. 2014

CONCUR 2014 – Concurrency Theory

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“…Section 8 concludes the paper. Preliminary results in the paper have been reported in three previous conference papers [17], [18], [19].…”

Section: Introductionmentioning

confidence: 85%

Asymptotic Perturbation Bounds for Probabilistic Model Checking with Empirically Determined Probability Parameters

Feng

Chen³

et al. 2016

IIEEE Trans. Software Eng.

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Abstract-Probabilistic model checking is a verification technique that has been the focus of intensive research for over a decade. One important issue with probabilistic model checking, which is crucial for its practical significance but is overlooked by the state-of-the-art largely, is the potential discrepancy between a stochastic model and the real-world system it represents when the model is built from statistical data. In the worst case, a tiny but nontrivial change to some model quantities might lead to misleading or even invalid verification results. To address this issue, in this paper, we present a mathematical characterization of the consequences of model perturbations on the verification distance. The formal model that we adopt is a parametric variant of discrete-time Markov chains equipped with a vector norm to measure the perturbation. Our main technical contributions include a closed-form formulation of asymptotic perturbation bounds, and computational methods for two arguably most useful forms of those bounds, namely linear bounds and quadratic bounds. We focus on verification of reachability properties but also address automata-based verification of omega-regular properties. We present the results of a selection of case studies that demonstrate that asymptotic perturbation bounds can accurately estimate maximum variations of verification results induced by model perturbations.

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Nested Reachability Approximation for Discrete-Time Markov Chains with Univariate Parameters

Rosenblum

2014

Automated Technology for Verification and Analysis

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Perturbation analysis of stochastic systems with empirical distribution parameters

Cited by 11 publications

References 31 publications

Perturbation Analysis in Verification of Discrete-Time Markov Chains

Perturbation Analysis in Verification of Discrete-Time Markov Chains

Asymptotic Perturbation Bounds for Probabilistic Model Checking with Empirically Determined Probability Parameters

Nested Reachability Approximation for Discrete-Time Markov Chains with Univariate Parameters

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