Interpretable Neural Causal Models with TRAM-DAGs

Beate Sick, Oliver Dürr
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:606-630, 2025.

Abstract

The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries on all three levels of Pearl’s causal hierarchy can be answered: $\mathcal{L}_1$ observational, $\mathcal{L}_2$ interventional, and $\mathcal{L}_3$ counterfactual. An essential aspect of modeling the SCM is to model the dependency of each variable on its causal parents. Traditionally this is done by parametric statistical models, such as linear or logistic regression models. This allows to handle all kinds of data types and fit interpretable models but bears the risk of introducing a bias due to the assumed rigid functional form. More recently neural causal models came up using neural networks (NNs) to model the causal relationships, allowing the estimation of nearly any underlying functional form without bias. However, current neural causal models are generally restricted to continuous variables and do not yield an interpretable form of the causal relationships. Transformation models range from simple statistical regressions to complex networks and can handle continuous, ordinal, and binary data. Here, we propose to use TRAMs to model the functional relationships in SCMs allowing us to bridge the gap between interpretability and flexibility in causal modeling. We call this method TRAM-DAG and assume currently that the underlying directed acyclic graph (DAG) is known. For the fully observed case, we benchmark TRAM-DAGs against state-of-the-art statistical and NN-based causal models. We show that TRAM-DAGs are interpretable but also achieve equal or superior performance in queries ranging from $\mathcal{L}_1$ to $\mathcal{L}_3$ in the causal hierarchy. For the continuous case, TRAM-DAGs allow for counterfactual queries for three common causal structures, including unobserved confounding.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-sick25a, title = {Interpretable Neural Causal Models with TRAM-DAGs}, author = {Sick, Beate and D\"{u}rr, Oliver}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {606--630}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/sick25a/sick25a.pdf}, url = {https://proceedings.mlr.press/v275/sick25a.html}, abstract = {The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries on all three levels of Pearl’s causal hierarchy can be answered: $\mathcal{L}_1$ observational, $\mathcal{L}_2$ interventional, and $\mathcal{L}_3$ counterfactual. An essential aspect of modeling the SCM is to model the dependency of each variable on its causal parents. Traditionally this is done by parametric statistical models, such as linear or logistic regression models. This allows to handle all kinds of data types and fit interpretable models but bears the risk of introducing a bias due to the assumed rigid functional form. More recently neural causal models came up using neural networks (NNs) to model the causal relationships, allowing the estimation of nearly any underlying functional form without bias. However, current neural causal models are generally restricted to continuous variables and do not yield an interpretable form of the causal relationships. Transformation models range from simple statistical regressions to complex networks and can handle continuous, ordinal, and binary data. Here, we propose to use TRAMs to model the functional relationships in SCMs allowing us to bridge the gap between interpretability and flexibility in causal modeling. We call this method TRAM-DAG and assume currently that the underlying directed acyclic graph (DAG) is known. For the fully observed case, we benchmark TRAM-DAGs against state-of-the-art statistical and NN-based causal models. We show that TRAM-DAGs are interpretable but also achieve equal or superior performance in queries ranging from $\mathcal{L}_1$ to $\mathcal{L}_3$ in the causal hierarchy. For the continuous case, TRAM-DAGs allow for counterfactual queries for three common causal structures, including unobserved confounding.} }
Endnote
%0 Conference Paper %T Interpretable Neural Causal Models with TRAM-DAGs %A Beate Sick %A Oliver Dürr %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-sick25a %I PMLR %P 606--630 %U https://proceedings.mlr.press/v275/sick25a.html %V 275 %X The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries on all three levels of Pearl’s causal hierarchy can be answered: $\mathcal{L}_1$ observational, $\mathcal{L}_2$ interventional, and $\mathcal{L}_3$ counterfactual. An essential aspect of modeling the SCM is to model the dependency of each variable on its causal parents. Traditionally this is done by parametric statistical models, such as linear or logistic regression models. This allows to handle all kinds of data types and fit interpretable models but bears the risk of introducing a bias due to the assumed rigid functional form. More recently neural causal models came up using neural networks (NNs) to model the causal relationships, allowing the estimation of nearly any underlying functional form without bias. However, current neural causal models are generally restricted to continuous variables and do not yield an interpretable form of the causal relationships. Transformation models range from simple statistical regressions to complex networks and can handle continuous, ordinal, and binary data. Here, we propose to use TRAMs to model the functional relationships in SCMs allowing us to bridge the gap between interpretability and flexibility in causal modeling. We call this method TRAM-DAG and assume currently that the underlying directed acyclic graph (DAG) is known. For the fully observed case, we benchmark TRAM-DAGs against state-of-the-art statistical and NN-based causal models. We show that TRAM-DAGs are interpretable but also achieve equal or superior performance in queries ranging from $\mathcal{L}_1$ to $\mathcal{L}_3$ in the causal hierarchy. For the continuous case, TRAM-DAGs allow for counterfactual queries for three common causal structures, including unobserved confounding.
APA
Sick, B. & Dürr, O.. (2025). Interpretable Neural Causal Models with TRAM-DAGs. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:606-630 Available from https://proceedings.mlr.press/v275/sick25a.html.

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