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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2306.07072 |
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| _version_ | 1866929652374700032 |
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| author | Kofnov, Andrey Moosbrugger, Marcel Stankovič, Miroslav Bartocci, Ezio Bura, Efstathia |
| author_facet | Kofnov, Andrey Moosbrugger, Marcel Stankovič, Miroslav Bartocci, Ezio Bura, Efstathia |
| contents | Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07072 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments Kofnov, Andrey Moosbrugger, Marcel Stankovič, Miroslav Bartocci, Ezio Bura, Efstathia Applications Numerical Analysis Symbolic Computation Statistics Theory 62G05, 62P30 G.3 Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art. |
| title | Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments |
| topic | Applications Numerical Analysis Symbolic Computation Statistics Theory 62G05, 62P30 G.3 |
| url | https://arxiv.org/abs/2306.07072 |