Learning Stable Digraphs from Sparse-Input Linear Structural Causal Models

Panagiotis Misiakos, Markus Püschel
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:4561-4594, 2026.

Abstract

We propose StableSpIn, a continuous optimization framework for learning potentially cyclic causal directed graphs (digraphs) in linear structural equation models via a spectral-radius constraint on the absolute adjacency matrix. Our motivation is twofold: first, stability is a natural requirement for linear structural models; second, the contractive cycles that stability induces facilitate the identifiability of digraphs. We formulate causal discovery as a likelihood-based optimization problem under a sparse-input assumption, yielding a scalable algorithm applicable to both cross-sectional and time-series data. Unlike prior continuous acyclicity constraints, our stability regularizer is cheaper to evaluate while accommodating general digraphs, yielding faster optimization in practice. Experiments on synthetic benchmarks show improved graph recovery over state-of-the-art baselines, and empirical studies on U.S., European, and Swiss equity markets reveal interpretable cyclic dependencies that persist across time windows. Our implementation is available at https://github.com/pmisiakos/StableSpIn.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-misiakos26a, title = {Learning Stable Digraphs from Sparse-Input Linear Structural Causal Models}, author = {Misiakos, Panagiotis and P\"{u}schel, Markus}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {4561--4594}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/misiakos26a/misiakos26a.pdf}, url = {https://proceedings.mlr.press/v337/misiakos26a.html}, abstract = {We propose StableSpIn, a continuous optimization framework for learning potentially cyclic causal directed graphs (digraphs) in linear structural equation models via a spectral-radius constraint on the absolute adjacency matrix. Our motivation is twofold: first, stability is a natural requirement for linear structural models; second, the contractive cycles that stability induces facilitate the identifiability of digraphs. We formulate causal discovery as a likelihood-based optimization problem under a sparse-input assumption, yielding a scalable algorithm applicable to both cross-sectional and time-series data. Unlike prior continuous acyclicity constraints, our stability regularizer is cheaper to evaluate while accommodating general digraphs, yielding faster optimization in practice. Experiments on synthetic benchmarks show improved graph recovery over state-of-the-art baselines, and empirical studies on U.S., European, and Swiss equity markets reveal interpretable cyclic dependencies that persist across time windows. Our implementation is available at https://github.com/pmisiakos/StableSpIn.} }
Endnote
%0 Conference Paper %T Learning Stable Digraphs from Sparse-Input Linear Structural Causal Models %A Panagiotis Misiakos %A Markus Püschel %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-misiakos26a %I PMLR %P 4561--4594 %U https://proceedings.mlr.press/v337/misiakos26a.html %V 337 %X We propose StableSpIn, a continuous optimization framework for learning potentially cyclic causal directed graphs (digraphs) in linear structural equation models via a spectral-radius constraint on the absolute adjacency matrix. Our motivation is twofold: first, stability is a natural requirement for linear structural models; second, the contractive cycles that stability induces facilitate the identifiability of digraphs. We formulate causal discovery as a likelihood-based optimization problem under a sparse-input assumption, yielding a scalable algorithm applicable to both cross-sectional and time-series data. Unlike prior continuous acyclicity constraints, our stability regularizer is cheaper to evaluate while accommodating general digraphs, yielding faster optimization in practice. Experiments on synthetic benchmarks show improved graph recovery over state-of-the-art baselines, and empirical studies on U.S., European, and Swiss equity markets reveal interpretable cyclic dependencies that persist across time windows. Our implementation is available at https://github.com/pmisiakos/StableSpIn.
APA
Misiakos, P. & Püschel, M.. (2026). Learning Stable Digraphs from Sparse-Input Linear Structural Causal Models. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:4561-4594 Available from https://proceedings.mlr.press/v337/misiakos26a.html.

Related Material