Causal Discovery with Linear Non-Gaussian Models under Measurement Error: Structural Identifiability Results

Causal discovery methods aim to recover the causal process that generated purely observa- tional data. Despite its successes on a number of real problems, the presence of measurement error in the observed data can produce seri- ous 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 reli- able causal discovery. It is still unknown to what extent the causal structure of relevant variables can be identified in principle. This study aims to take a step towards filling that void. We assume that the underlining pro- cess or the measurement-error free variables follows a linear, non-Guassian causal model, and show that the so-called ordered group decomposition of the causal model, which con- tains major causal information, is identifiable. The causal structure identifiability is further improved with different types of sparsity con- straints on the causal structure. Finally, we give rather mild conditions under which the whole causal structure is fully identifiable.