Density Elicitation with applications in Probabilistic Loops

04/17/2023
by   Andrey Kofnov, et al.
0

Probabilistic loops can be employed to implement and to model different processes ranging from software to cyber-physical systems. One main challenge is how to automatically estimate the distribution of the underlying continuous random variables symbolically and without sampling. We develop an approach, which we call K-series estimation, to approximate statically the joint and marginal distributions of a vector of random variables updated in a probabilistic non-nested loop with polynomial and non-polynomial assignments. Our approach is a general estimation method for an unknown probability density function with bounded support. It naturally complements algorithms for automatic derivation of moments in probabilistic loops such as <cit.>. Its only requirement is a finite number of moments of the unknown density. We show that Gram-Charlier (GC) series, a widely used estimation method, is a special case of K-series when the normal probability density function is used as reference distribution. We provide also a formulation suitable for estimating both univariate and multivariate distributions. We demonstrate the feasibility of our approach using multiple examples from the literature.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset