Linear Causal Disentanglement via Interventions

Chandler Squires, Anna Seigal, Salil S Bhate, Caroline Uhler
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:32540-32560, 2023.

Abstract

Causal disentanglement seeks a representation of data involving latent variables that are related via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement. We show that the method accurately recovers a latent causal model on synthetic and semi-synthetic data and we illustrate a use case on a dataset of single-cell RNA sequencing measurements.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-squires23a, title = {Linear Causal Disentanglement via Interventions}, author = {Squires, Chandler and Seigal, Anna and Bhate, Salil S and Uhler, Caroline}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {32540--32560}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/squires23a/squires23a.pdf}, url = {https://proceedings.mlr.press/v202/squires23a.html}, abstract = {Causal disentanglement seeks a representation of data involving latent variables that are related via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement. We show that the method accurately recovers a latent causal model on synthetic and semi-synthetic data and we illustrate a use case on a dataset of single-cell RNA sequencing measurements.} }
Endnote
%0 Conference Paper %T Linear Causal Disentanglement via Interventions %A Chandler Squires %A Anna Seigal %A Salil S Bhate %A Caroline Uhler %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-squires23a %I PMLR %P 32540--32560 %U https://proceedings.mlr.press/v202/squires23a.html %V 202 %X Causal disentanglement seeks a representation of data involving latent variables that are related via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement. We show that the method accurately recovers a latent causal model on synthetic and semi-synthetic data and we illustrate a use case on a dataset of single-cell RNA sequencing measurements.
APA
Squires, C., Seigal, A., Bhate, S.S. & Uhler, C.. (2023). Linear Causal Disentanglement via Interventions. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:32540-32560 Available from https://proceedings.mlr.press/v202/squires23a.html.

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