Identifiability of Sparse Causal Effects using Instrumental Variables
- URL: http://arxiv.org/abs/2203.09380v1
- Date: Thu, 17 Mar 2022 15:15:52 GMT
- Title: Identifiability of Sparse Causal Effects using Instrumental Variables
- Authors: Niklas Pfister and Jonas Peters
- Abstract summary: We prove that the causal coefficient becomes identifiable under weak conditions and may even be identified in models, where the number of instruments is as small as the number of causal parents.
As an estimator, we propose spaceIV and prove that it consistently estimates the causal effect if the model is identifiable and evaluate its performance on simulated data.
- Score: 5.368313160283353
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Exogenous heterogeneity, for example, in the form of instrumental variables
can help us learn a system's underlying causal structure and predict the
outcome of unseen intervention experiments. In this paper, we consider linear
models in which the causal effect from covariates $X$ on a response $Y$ is
sparse. We prove that the causal coefficient becomes identifiable under weak
conditions and may even be identified in models, where the number of
instruments is as small as the number of causal parents. We also develop
graphical criteria under which the identifiability holds with probability one
if the edge coefficients are sampled randomly from a distribution that is
absolutely continuous with respect to Lebesgue measure. As an estimator, we
propose spaceIV and prove that it consistently estimates the causal effect if
the model is identifiable and evaluate its performance on simulated data.
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