Information-Theoretic Limits of Causal Discovery from Observational Data

Abstract

Causal discovery, the inference of causal relationships from purely observational data, is a cornerstone of scientific inquiry across diverse fields. Despite significant algorithmic advancements, a comprehensive understanding of the fundamental information-theoretic limits -- what can be discovered and with what confidence -- remains an open challenge. This paper presents an integrated exploration of these inherent limits in causal discovery from observational data, systematically delineating theoretical boundaries and intrinsic challenges. We leverage information theory concepts, including entropy, mutual information, and conditional independence, to quantify the information content relevant to causal structures. By examining the sufficiency of information encoded in observed joint distributions, we investigate conditions under which unique causal graphs are identifiable and, conversely, when ambiguity is unavoidable. We discuss the implications of finite sample sizes, noise, and latent confounding variables on the identifiability and accuracy of causal inference, framing these challenges within an information-theoretic context. Our analysis offers insights into the intrinsic limitations of current and future causal discovery algorithms, highlighting the necessity for stronger assumptions or additional interventional data when observational data alone is insufficient to resolve causal ambiguities.