Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

TL;DR

This paper introduces an automatic backward filtering forward guiding (BFFG) paradigm for probabilistic graphical models with Markov processes, enabling efficient inference of latent states and parameters across various complex stochastic systems.

Contribution

The paper presents a novel BFFG framework that transforms generative models into guided models for improved inference, applicable to diverse Markov process-based models.

Findings

Effective inference in Markov chains and particle systems

Versatile application to state space models and diffusions

Enhanced sampling efficiency in probabilistic models

Abstract

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.