Karimi, A., Moosbrugger, M., Stankovič, M., Kovács, L., Bartocci, E., & Bura, E. (2022). Distribution Estimation for Probabilistic Loops. In E. Ábrahám & M. Paolieri (Eds.), Quantitative Evaluation of Systems (pp. 26–42). Springer-Verlag. https://doi.org/10.1007/978-3-031-16336-4_2
E105-08 - Forschungsbereich Angewandte Statistik E192-04 - Forschungsbereich Formal Methods in Systems Engineering E191-01 - Forschungsbereich Cyber-Physical Systems E101-03 - Forschungsbereich Scientific Computing and Modelling
International Conference on Quantitative Evaluation of Systems (QEST 2022)s
en
Veranstaltungszeitraum:
12-Sep-2022 - 16-Sep-2022
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Veranstaltungsort:
Warsaw, Polen
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Umfang:
17
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Verlag:
Springer-Verlag, Berlin, Heidelberg
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Peer Reviewed:
Ja
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Keywords:
Distribution Estimation; Probabilistic Loops; Quantitative Evaluation
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Abstract:
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and Gram-Charlier series, to estimate the distributions of the loop’s random variables. We measure the accuracy of our distribution estimation by comparing the resulting distributions using exact and estimated moments of the probabilistic loop, and performing statistical tests. We evaluate our method on several probabilistic loops with polynomial updates over random variables drawing from common probability distributions, including examples implementing financial and biological models. For this, we leverage symbolic approaches to compute exact higher-order moments of loops as well as use sampling-based techniques to estimate moments from loop executions. Our experimental results provide practical evidence of the accuracy of our method for estimating distributions of probabilistic loop outputs.
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Projekttitel:
Distribution Recovery for Invariant Generation of Probabilistic Programs: ICT19-018 (WWTF Wiener Wissenschafts-, Forschu und Technologiefonds) Automated Reasoning with Theories and Induction for Software Technologies: ERC Consolidator Grant 2020 (European Commission) Prognostizierung einer suffizienten Dimensions-Reduktions-Methodik: P 30690-N35 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Forschungsschwerpunkte:
Logic and Computation: 33% Mathematical and Algorithmic Foundations: 34% Computer Engineering and Software-Intensive Systems: 33%