Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity

David Strieder, Mathias Drton
Proceedings of The 12th International Conference on Probabilistic Graphical Models, PMLR 246:213-230, 2024.

Abstract

A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting variables. A directed graph naturally represents these models and reflects the underlying causal structure. However, classical identifiability results suggest that, without conducting additional experiments, this causal graph can only be identified up to a Markov equivalence class of indistinguishable models. Recent research has shown that focusing on linear relations with equal error variances can enable the identification of the causal structure from mere observational data. Nonetheless, practitioners are often primarily interested in the effects of specific interventions, rendering the complete identification of the causal structure unnecessary. In this work, we investigate the extent to which less restrictive assumptions of partial homoscedasticity are sufficient for identifying the causal effects of interest. Furthermore, we construct mathematically rigorous confidence regions for total causal effects under structure uncertainty and explore the performance gain of relying on stricter error assumptions in a simulation study.

Cite this Paper

BibTeX
@InProceedings{pmlr-v246-strieder24a, title = {Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity}, author = {Strieder, David and Drton, Mathias}, booktitle = {Proceedings of The 12th International Conference on Probabilistic Graphical Models}, pages = {213--230}, year = {2024}, editor = {Kwisthout, Johan and Renooij, Silja}, volume = {246}, series = {Proceedings of Machine Learning Research}, month = {11--13 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v246/main/assets/strieder24a/strieder24a.pdf}, url = {https://proceedings.mlr.press/v246/strieder24a.html}, abstract = {A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting variables. A directed graph naturally represents these models and reflects the underlying causal structure. However, classical identifiability results suggest that, without conducting additional experiments, this causal graph can only be identified up to a Markov equivalence class of indistinguishable models. Recent research has shown that focusing on linear relations with equal error variances can enable the identification of the causal structure from mere observational data. Nonetheless, practitioners are often primarily interested in the effects of specific interventions, rendering the complete identification of the causal structure unnecessary. In this work, we investigate the extent to which less restrictive assumptions of partial homoscedasticity are sufficient for identifying the causal effects of interest. Furthermore, we construct mathematically rigorous confidence regions for total causal effects under structure uncertainty and explore the performance gain of relying on stricter error assumptions in a simulation study.} }
Endnote
%0 Conference Paper %T Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity %A David Strieder %A Mathias Drton %B Proceedings of The 12th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2024 %E Johan Kwisthout %E Silja Renooij %F pmlr-v246-strieder24a %I PMLR %P 213--230 %U https://proceedings.mlr.press/v246/strieder24a.html %V 246 %X A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting variables. A directed graph naturally represents these models and reflects the underlying causal structure. However, classical identifiability results suggest that, without conducting additional experiments, this causal graph can only be identified up to a Markov equivalence class of indistinguishable models. Recent research has shown that focusing on linear relations with equal error variances can enable the identification of the causal structure from mere observational data. Nonetheless, practitioners are often primarily interested in the effects of specific interventions, rendering the complete identification of the causal structure unnecessary. In this work, we investigate the extent to which less restrictive assumptions of partial homoscedasticity are sufficient for identifying the causal effects of interest. Furthermore, we construct mathematically rigorous confidence regions for total causal effects under structure uncertainty and explore the performance gain of relying on stricter error assumptions in a simulation study.
APA
Strieder, D. & Drton, M.. (2024). Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity. Proceedings of The 12th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 246:213-230 Available from https://proceedings.mlr.press/v246/strieder24a.html.

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