A0239
Title: Exact and approximate moment derivation for probabilistic loops with non-polynomial assignments
Authors: Efstathia Bura - Vienna University of Technology (Austria) [presenting]
Andrey Kofnov - TU Wien (Austria)
Ezio Bartocci - Vienna University of Technology (Austria)
Marcel Moosbrugger - Vienna University of Technology (Austria)
Miroslav Stankovic - TU Wien (Austria)
Abstract: Probabilistic programs (PPs) are modern tools to automate statistical modeling. They are becoming ubiquitous in AI applications, security/privacy protocols and stochastic dynamical system modeling. 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 compute automatically and without sampling moment-based invariants for such probabilistic programs as a closed-form solution in loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate moment propagation method 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 all orders 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.
