Identifiability of sparse causal effects using instrumental variables

Niklas Pfister, Jonas Peters
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1613-1622, 2022.

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 provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and $Y$ is childless. 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. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-pfister22a, title = {Identifiability of sparse causal effects using instrumental variables}, author = {Pfister, Niklas and Peters, Jonas}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1613--1622}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/pfister22a/pfister22a.pdf}, url = {https://proceedings.mlr.press/v180/pfister22a.html}, 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 provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and $Y$ is childless. 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. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.} }
Endnote
%0 Conference Paper %T Identifiability of sparse causal effects using instrumental variables %A Niklas Pfister %A Jonas Peters %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-pfister22a %I PMLR %P 1613--1622 %U https://proceedings.mlr.press/v180/pfister22a.html %V 180 %X 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 provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and $Y$ is childless. 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. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.
APA
Pfister, N. & Peters, J.. (2022). Identifiability of sparse causal effects using instrumental variables. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1613-1622 Available from https://proceedings.mlr.press/v180/pfister22a.html.

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