Robust identifiability in linear structural equation models of causal inference

Karthik A. Sankararaman, Anand Louis, Navin Goyal
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1728-1737, 2022.

Abstract

We consider the problem of robust parameter estimation from observational data in the context of linear structural equation models (LSEMs). Under various conditions on LSEMs and the model parameters the prior work provides efficient algorithms to recover the parameters. However, these results are often about generic identifiability. In practice, generic identifiability is not sufficient and we need robust identifiability: small changes in the observational data should not affect the parameters by a huge amount. Robust identifiability has received far less attention and remains poorly understood. Sankararaman et al. (2019) recently provided a set of sufficient conditions on parameters under which robust identifiability is feasible. However, a limitation of their work is that their results only apply to a small sub-class of LSEMs, called “bow-free paths.” In this work, we show that for any “bow-free model”, in all but $\frac{1}{\poly(n)}$-measure of instances robust identifiability holds. Moreover, whenever an instance is robustly identifiable, the algorithm proposed in Foygel et al., (2012) can be used to recover the parameters in a robust fashion. In contrast, for generic identifiability Foygel et al., (2012) proved that with measure $1$, instances are generically identifiable. Thus, we show that robust identifiability is a strictly harder problem than generic identifiability. Finally, we validate our results on both simulated and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-sankararaman22a, title = {Robust identifiability in linear structural equation models of causal inference}, author = {Sankararaman, Karthik A. and Louis, Anand and Goyal, Navin}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1728--1737}, 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/sankararaman22a/sankararaman22a.pdf}, url = {https://proceedings.mlr.press/v180/sankararaman22a.html}, abstract = {We consider the problem of robust parameter estimation from observational data in the context of linear structural equation models (LSEMs). Under various conditions on LSEMs and the model parameters the prior work provides efficient algorithms to recover the parameters. However, these results are often about generic identifiability. In practice, generic identifiability is not sufficient and we need robust identifiability: small changes in the observational data should not affect the parameters by a huge amount. Robust identifiability has received far less attention and remains poorly understood. Sankararaman et al. (2019) recently provided a set of sufficient conditions on parameters under which robust identifiability is feasible. However, a limitation of their work is that their results only apply to a small sub-class of LSEMs, called “bow-free paths.” In this work, we show that for any “bow-free model”, in all but $\frac{1}{\poly(n)}$-measure of instances robust identifiability holds. Moreover, whenever an instance is robustly identifiable, the algorithm proposed in Foygel et al., (2012) can be used to recover the parameters in a robust fashion. In contrast, for generic identifiability Foygel et al., (2012) proved that with measure $1$, instances are generically identifiable. Thus, we show that robust identifiability is a strictly harder problem than generic identifiability. Finally, we validate our results on both simulated and real-world datasets.} }
Endnote
%0 Conference Paper %T Robust identifiability in linear structural equation models of causal inference %A Karthik A. Sankararaman %A Anand Louis %A Navin Goyal %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-sankararaman22a %I PMLR %P 1728--1737 %U https://proceedings.mlr.press/v180/sankararaman22a.html %V 180 %X We consider the problem of robust parameter estimation from observational data in the context of linear structural equation models (LSEMs). Under various conditions on LSEMs and the model parameters the prior work provides efficient algorithms to recover the parameters. However, these results are often about generic identifiability. In practice, generic identifiability is not sufficient and we need robust identifiability: small changes in the observational data should not affect the parameters by a huge amount. Robust identifiability has received far less attention and remains poorly understood. Sankararaman et al. (2019) recently provided a set of sufficient conditions on parameters under which robust identifiability is feasible. However, a limitation of their work is that their results only apply to a small sub-class of LSEMs, called “bow-free paths.” In this work, we show that for any “bow-free model”, in all but $\frac{1}{\poly(n)}$-measure of instances robust identifiability holds. Moreover, whenever an instance is robustly identifiable, the algorithm proposed in Foygel et al., (2012) can be used to recover the parameters in a robust fashion. In contrast, for generic identifiability Foygel et al., (2012) proved that with measure $1$, instances are generically identifiable. Thus, we show that robust identifiability is a strictly harder problem than generic identifiability. Finally, we validate our results on both simulated and real-world datasets.
APA
Sankararaman, K.A., Louis, A. & Goyal, N.. (2022). Robust identifiability in linear structural equation models of causal inference. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1728-1737 Available from https://proceedings.mlr.press/v180/sankararaman22a.html.

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