Generalized Criterion for Identifiability of Additive Noise Models Using Majorization

Aramayis Dallakyan, Yang Ni
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:37-45, 2025.

Abstract

The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing identifiability criteria in the literature that employ (conditional) variances as measures of uncertainty in (conditional) distributions. For linear structural equation models, we present a new algorithm that leverages the concept of weak majorization applied to the diagonal elements of the Cholesky factor of the covariance matrix to learn a topological ordering of variables. Through extensive simulations and the analysis of bank connectivity data, we provide evidence of the effectiveness of our approach in successfully recovering DAGs. The code for reproducing the results in this paper is available in Supplementary Materials.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-dallakyan25a, title = {Generalized Criterion for Identifiability of Additive Noise Models Using Majorization}, author = {Dallakyan, Aramayis and Ni, Yang}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {37--45}, 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/dallakyan25a/dallakyan25a.pdf}, url = {https://proceedings.mlr.press/v258/dallakyan25a.html}, abstract = {The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing identifiability criteria in the literature that employ (conditional) variances as measures of uncertainty in (conditional) distributions. For linear structural equation models, we present a new algorithm that leverages the concept of weak majorization applied to the diagonal elements of the Cholesky factor of the covariance matrix to learn a topological ordering of variables. Through extensive simulations and the analysis of bank connectivity data, we provide evidence of the effectiveness of our approach in successfully recovering DAGs. The code for reproducing the results in this paper is available in Supplementary Materials.} }
Endnote
%0 Conference Paper %T Generalized Criterion for Identifiability of Additive Noise Models Using Majorization %A Aramayis Dallakyan %A Yang Ni %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-dallakyan25a %I PMLR %P 37--45 %U https://proceedings.mlr.press/v258/dallakyan25a.html %V 258 %X The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing identifiability criteria in the literature that employ (conditional) variances as measures of uncertainty in (conditional) distributions. For linear structural equation models, we present a new algorithm that leverages the concept of weak majorization applied to the diagonal elements of the Cholesky factor of the covariance matrix to learn a topological ordering of variables. Through extensive simulations and the analysis of bank connectivity data, we provide evidence of the effectiveness of our approach in successfully recovering DAGs. The code for reproducing the results in this paper is available in Supplementary Materials.
APA
Dallakyan, A. & Ni, Y.. (2025). Generalized Criterion for Identifiability of Additive Noise Models Using Majorization. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:37-45 Available from https://proceedings.mlr.press/v258/dallakyan25a.html.

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