Reconstruction of Causal Networks by Set Covering

TL;DR

This paper introduces a method for reconstructing minimal causal networks from data using local set covering approximations, extended to handle noise, and validated on synthetic epidemiological data.

Contribution

The paper presents a novel network reconstruction algorithm based on set covering, enabling local inference of node neighborhoods and robustness to noisy data.

Findings

Successfully reconstructs networks consistent with data

Handles noisy data via Minimum Description Length

Effective on synthetic epidemiological models

Abstract

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.