Differentiable Causal Structure Learning with Identifiability by NOTIME

Jeroen Berrevoets, Jakob Raymaekers, Mihaela van der Schaar, Tim Verdonck, Ruicong Yao
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3115-3123, 2025.

Abstract

The introduction of the NOTEARS algorithm resulted in a wave of research on differentiable Directed Acyclic Graph (DAG) learning. Differentiable DAG learning transforms the combinatorial problem of identifying the DAG underlying a Structural Causal Model (SCM) into a constrained continuous optimization problem. Being differentiable, these problems can be solved using gradient-based tools which allow integration into other differentiable objectives. However, in contrast to classical constrained-based algorithms, the identifiability properties of differentiable algorithms are poorly understood. We illustrate that even in the well-known Linear Non-Gaussian Additive Model (LiNGAM), the current state-of-the-art methods do not identify the true underlying DAG. To address the issue, we propose NOTIME (\emph{Non-combinatorial Optimization of Trace exponential and Independence MEasures}), the first differentiable DAG learning algorithm with \emph{provable} identifiability guarantees under the LiNGAM by building on a measure of (joint) independence. With its identifiability guarantees, NOTIME remains invariant to normalization of the data on a population level, a property lacking in existing methods. NOTIME compares favourably against NOTEARS and other (scale-invariant) differentiable DAG learners, across different noise distributions and normalization procedures. Introducing the first identifiability guarantees to general LiNGAM is an important step towards practical adoption of differentiable DAG learners.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-berrevoets25a, title = {Differentiable Causal Structure Learning with Identifiability by NOTIME}, author = {Berrevoets, Jeroen and Raymaekers, Jakob and van der Schaar, Mihaela and Verdonck, Tim and Yao, Ruicong}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3115--3123}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/berrevoets25a/berrevoets25a.pdf}, url = {https://proceedings.mlr.press/v258/berrevoets25a.html}, abstract = {The introduction of the NOTEARS algorithm resulted in a wave of research on differentiable Directed Acyclic Graph (DAG) learning. Differentiable DAG learning transforms the combinatorial problem of identifying the DAG underlying a Structural Causal Model (SCM) into a constrained continuous optimization problem. Being differentiable, these problems can be solved using gradient-based tools which allow integration into other differentiable objectives. However, in contrast to classical constrained-based algorithms, the identifiability properties of differentiable algorithms are poorly understood. We illustrate that even in the well-known Linear Non-Gaussian Additive Model (LiNGAM), the current state-of-the-art methods do not identify the true underlying DAG. To address the issue, we propose NOTIME (\emph{Non-combinatorial Optimization of Trace exponential and Independence MEasures}), the first differentiable DAG learning algorithm with \emph{provable} identifiability guarantees under the LiNGAM by building on a measure of (joint) independence. With its identifiability guarantees, NOTIME remains invariant to normalization of the data on a population level, a property lacking in existing methods. NOTIME compares favourably against NOTEARS and other (scale-invariant) differentiable DAG learners, across different noise distributions and normalization procedures. Introducing the first identifiability guarantees to general LiNGAM is an important step towards practical adoption of differentiable DAG learners.} }
Endnote
%0 Conference Paper %T Differentiable Causal Structure Learning with Identifiability by NOTIME %A Jeroen Berrevoets %A Jakob Raymaekers %A Mihaela van der Schaar %A Tim Verdonck %A Ruicong Yao %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-berrevoets25a %I PMLR %P 3115--3123 %U https://proceedings.mlr.press/v258/berrevoets25a.html %V 258 %X The introduction of the NOTEARS algorithm resulted in a wave of research on differentiable Directed Acyclic Graph (DAG) learning. Differentiable DAG learning transforms the combinatorial problem of identifying the DAG underlying a Structural Causal Model (SCM) into a constrained continuous optimization problem. Being differentiable, these problems can be solved using gradient-based tools which allow integration into other differentiable objectives. However, in contrast to classical constrained-based algorithms, the identifiability properties of differentiable algorithms are poorly understood. We illustrate that even in the well-known Linear Non-Gaussian Additive Model (LiNGAM), the current state-of-the-art methods do not identify the true underlying DAG. To address the issue, we propose NOTIME (\emph{Non-combinatorial Optimization of Trace exponential and Independence MEasures}), the first differentiable DAG learning algorithm with \emph{provable} identifiability guarantees under the LiNGAM by building on a measure of (joint) independence. With its identifiability guarantees, NOTIME remains invariant to normalization of the data on a population level, a property lacking in existing methods. NOTIME compares favourably against NOTEARS and other (scale-invariant) differentiable DAG learners, across different noise distributions and normalization procedures. Introducing the first identifiability guarantees to general LiNGAM is an important step towards practical adoption of differentiable DAG learners.
APA
Berrevoets, J., Raymaekers, J., van der Schaar, M., Verdonck, T. & Yao, R.. (2025). Differentiable Causal Structure Learning with Identifiability by NOTIME. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3115-3123 Available from https://proceedings.mlr.press/v258/berrevoets25a.html.

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