We consider the problem of learning a causal graph in the presence of measurement error. This setting is for example common in genomics, where gene expression is corrupted through the measurement process. We develop a provably consistent procedure for estimating the causal structure in a linear Gaussian structural equation model from corrupted observations on its nodes, under a variety of measurement error models. We provide an estimator based on the method-of-moments, which can be used in conjunction with constraint-based causal structure discovery algorithms. We prove asymptotic consistency of the procedure and also discuss finite-sample considerations. We demonstrate our method's performance through simulations and on real data, where we recover the underlying gene regulatory network from zero-inflated single-cell RNA-seq data.
@article{arxiv.1906.00928,
title = {Anchored Causal Inference in the Presence of Measurement Error},
author = {Basil Saeed and Anastasiya Belyaeva and Yuhao Wang and Caroline Uhler},
journal= {arXiv preprint arXiv:1906.00928},
year = {2019}
}