Particle Flow Bayes' Rule
This work addresses the challenge of efficient and generalizable Bayesian inference for applications in machine learning and statistics, representing a novel method rather than an incremental improvement.
The authors tackled the problem of Bayesian inference by introducing a particle flow realization of Bayes' rule using an ODE-based neural operator to transport particles from prior to posterior, and demonstrated its generalization ability across different priors, observations, and sequential inference in canonical and high-dimensional examples.
We 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. 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 sequential Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.