Inference in conditioned dynamics through causality restoration

Abstract

Estimating observables from conditioned dynamics is typically computationally hard. While obtaining independent samples efficiently from unconditioned dynamics is usually feasible, most of them do not satisfy the imposed conditions and must be discarded.On the other hand, conditioning breaks the causal properties of the dynamics, which ultimately renders the sampling of the conditioned dynamics non-trivial and inefficient. In this work, a Causal Variational Approach is proposed, as an approximate method to generate independent samples from a conditioned distribution. The procedure relies on learning the parameters of a generalized dynamical model that optimally describes the conditioned distribution in a variational sense. The outcome is an effective and unconditioned dynamical model from which one can trivially obtain independent samples, effectively restoring the causality of the conditioned dynamics. The consequences are twofold: the method allows one to efficiently compute observables from the conditioned dynamics by averaging over independent samples; moreover, it provides an effective unconditioned distribution that is easy to interpret. This approximation can be applied virtually to any dynamics. The application of the method to epidemic inference is discussed in detail. The results of direct comparison with state-of-the-art inference methods, including the soft-margin approach and mean-field methods, are promising.

Protect Your Score: Contact-Tracing with Differential Privacy Guarantees

“…Herbrich, Rastogi, and Vollgraf (2020) investigate statistical contact tracing using Gibbs sampling and show results on a simulator based on stochastic block models. Braunstein et al (2023) propose an inference model similar to belief propagation but do not test on COVID19 simulators. Most similar to ours, Baker et al (2021) propose statistical contact tracing using belief propagation on a collapsed graph.…”