Title: Causal inference in partially linear structural equation models with Gaussian noise
Authors: Dominik Rothenhaeusler - ETH Zurich (Switzerland) [presenting]
Peter Buehlmann - ETH Zurich (Switzerland)
Jan Ernest - ETH Zurich (Switzerland)
Abstract: The identifiability and estimation of partially linear additive structural equation models with Gaussian noise (PLSEMs) is considered. Existing identifiability results in the framework of additive SEMs with Gaussian noise are limited to linear and nonlinear SEMs, which can be considered as special cases of PLSEMs with vanishing non-parametric or parametric part, respectively. We close the wide gap between these two special cases by providing a comprehensive theory of the identifiability of PLSEMs by means of (A) a graphical, (B) a transformational, (C) a functional and (D) a causal ordering characterization of PLSEMs that generate a given distribution P. In particular, the characterizations (C) and (D) answer the fundamental question to which extent nonlinear functions in additive SEMs with Gaussian noise restrict the set of potential causal models and hence influence the identifiability.