Bidirectional compositionality in inference and stochastic optimisation

Abstract: Bayesian inference, entropy-regularised optimal transport and optimal control are linked via a variational formalism. The laws of compositionality of the formalism are of optical nature: the Bellman principle leads to bidirectional (backward-forward) representation of the posterior, the optimally controlled process or the optimal transport scheme. The Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2020) is an extension which incorporates a Monte Carlo element. This allows to formulate a set of elementary (and, by Monte Carlo, tractable) transformation rules of functorial nature suitable for automatisation in probabilistic programming.

category theoryprobabilitystatistics theory

Audience: researchers in the topic

( slides | video )

Intercats: Seminar on Categorical Interaction