Lower Bounds on Information Requirements for Causal Network Inference

Abstract

Recovery of the causal structure of dynamic networks from noisy measurements has long been a problem of interest across many areas of science and engineering. Many algorithms have been proposed, but there is little work that compares the performance of the algorithms to converse bounds in a non-asymptotic setting. As a step to address this problem, this paper gives lower bounds on the error probability for causal network support recovery in a linear Gaussian setting. The bounds are based on Monte Carlo estimation of receiver operating characteristic (ROC) curves based on likelihood ratio samples assuming side information is available. The estimated ROC curves and curves obtained through the use of Bhattacharyya coefficients or Kullback--Leibler divergences are also compared.