Mental Models 4 Life

A few colleagues and I have just completed a new research paper titled Factored Conditional Filtering: Tracking States and Estimating Parameters in High-Dimensional Spaces. The research took over 3 years and I am really excited about the underlying theory and its possible applications. In particular, the paper shows how we can lift’ Bayesian filtering to structured environments, with agent histories, transition models, and observations expressed in a formal knowledge representation framework. (Our chosen formalism is modal higher-order logic but it’s easy to swap other logical formalisms in.) Bayesian filtering is, of course, the gold standard in low-level data fusion and tracking from sensor data. In high-level structured logical environments, the equivalent data-fusion and tracking problem is addressed mostly in the belief-revision literature and the dominant theory there is still the AGM model from around 1985. I hope our new paper paves a way to the use of Bayesian filtering up the knowledge representation chain, hopefully leading to a unified way of handling tracking, belief revision and parameter learning in both low-level sensor data and high-level semantic concepts.

Here’s the paper.

https://arxiv.org/abs/2206.02178

Here’s the abstract:

This paper introduces the factored conditional filter, a new filtering algorithm for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithm is used to estimate parameters and the factored nature is used to decompose the state space into low-dimensional subspaces in such a way that filtering on these subspaces gives distributions whose product is a good approximation to the distribution on the entire state space. The conditions for successful application of the algorithm are that observations be available at the subspace level and that the transition model can be factored into local transition models that are approximately confined to the subspaces; these conditions are widely satisfied in computer science, engineering, and geophysical filtering applications. We give experimental results on tracking epidemics and estimating parameters in large contact networks that show the effectiveness of our approach.