Lower Bounds on Information Requirements for Causal Network Inference

TL;DR

This paper establishes fundamental lower bounds on the error probability for recovering causal network structures from noisy data in linear Gaussian models, providing a benchmark for evaluating causal inference algorithms.

Contribution

It introduces non-asymptotic lower bounds on causal network support recovery error, using Monte Carlo methods and information-theoretic measures for the first time in this context.

Findings

Lower bounds on error probability are derived for causal network inference.

Monte Carlo estimation effectively approximates ROC curves for these bounds.

Information-theoretic measures like Bhattacharyya and KL divergences are compared for accuracy.

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.