Causal inference in partially linear structural equation models
By Dominik Rothenhausler, Jan Ernest, Peter Buhlmann. 2016
34 citations recorded by the source corpus.
We consider the identifiability and estimation of partially linear additive structural equation models with Gaussian noise (PLSEMs). 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 nonparametric 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. 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. On the basis of the transformational characterization (B) we provide a score-based estimation procedure that outputs the graphical representation (A) of the distribution equivalence class of a given PLSEM. We derive its (high-dimensional) consistency and demonstrate its performance on simulated datasets.
Subfields: Artificial Intelligence, Statistics and Probability
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In Artificial Intelligence
- Bryon Aragam
- Eric P. Xing
- Pradeep Ravikumar
- Xun Zheng
- Chen Dan
- Yoshua Bengio
- Simon Lacoste-Julien
- Bernhard Schölkopf
In Statistics and Probability
- Eric P. Xing
- Bryon Aragam
- Pradeep Ravikumar
- Xun Zheng
- Chen Dan
- Francis R. Bach
- Martin J. Wainwright
- Rodolphe Jenatton
Citations in the corpus
- Learning Sparse Nonparametric DAGs (2019, methodology): “Related work The problem of learning nonlinear and nonparametric DAGs from data has generated significant interest in recent years, including additive models (Bühlmann et al., 2014; Voorman et al., 2014; Ernest et al., 2016), additive noise models (Hoyer et al.”