Kun Zhang (Carnegie Mellon Univerisity), Jiji Zhang (Lingnan University), Clark Glymour (Carnegie Mellon Univerisity)
Causal discovery methods aim to recover the causal process that generated purely observational data. Despite its successes on a number of real problems, the presence of measurement error in the observed data can produce serious mistakes in the output of various causal discovery methods. Given the ubiquity of measurement error caused by instruments or proxies used in the measuring process, this problem is one of the main obstacles to reliable causal discovery. It is still unknown to what extent the causal structure of relevant variables can be identified in principle, let alone how to develop a practical algorithm to solve this problem. This study aims to take a step towards filling that void. We investigate assumptions that suffice for it to be possible in principle to identify causal relations from observed data. Inspired by our theoretical results, we also present a set of methods for causal discovery under measurement error.
