Compositionality in algorithms for smoothing
Category Theory
2026-03-25 v5 Methodology
Abstract
Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics by demonstrating that the forward and backwards map together define a functor from a category of Markov kernels into a category of optics, which is furthermore lax monoidal in the case when the guiding kernels coincide with the generative dynamics
Cite
@article{arxiv.2303.13865,
title = {Compositionality in algorithms for smoothing},
author = {Moritz Schauer and Frank van der Meulen and Andi Q. Wang},
journal= {arXiv preprint arXiv:2303.13865},
year = {2026}
}