Universal Learning of Stochastic Dynamics for Exact Belief Propagation using Bernstein Normalizing Flows
It addresses the challenge of reasoning under uncertainty in stochastic systems where analytical solutions are intractable, offering a novel approach for domains requiring precise predictions.
The paper tackles the problem of learning stochastic dynamics models from data to enable exact belief propagation for nonlinear systems, achieving superior performance over state-of-the-art methods, particularly for highly nonlinear systems with non-additive, non-Gaussian noise.
Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring approximate methods. When the system model is unknown and must be learned from data, a key question arises: can we learn a model that (i) universally approximates general nonlinear stochastic dynamics, and (ii) supports analytical belief propagation? This paper establishes the theoretical foundations for a class of models that satisfy both properties. The proposed approach combines the expressiveness of normalizing flows for density estimation with the analytical tractability of Bernstein polynomials. Empirical results show the efficacy of our learned model over state-of-the-art data-driven methods for belief propagation, especially for highly non-linear systems with non-additive, non-Gaussian noise.