Meta Particle Flow for Sequential Bayesian Inference

In many data analysis tasks, it is important to estimate unknown quantities from observations. Given prior knowledge and likelihood, the essence of Bayesian inference is to compute the posterior by Baye's rule. In many real problems, observations arrive sequentially and thus online Bayesian inference needs to be performed recursively. In this talk, I will present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists and its neural parameterization can be trained in a meta-learning framework, allowing this operator to reason about the effect of an individual observation on the posterior, and thus generalize across different priors, observations and to online Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.