Causal Discovery with Score Matching on Additive Models with Arbitrary Noise

Francesco Montagna, Nicoletta Noceti, Lorenzo Rosasco, Kun Zhang, Francesco Locatello
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:726-751, 2023.

Abstract

Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-montagna23a, title = {Causal Discovery with Score Matching on Additive Models with Arbitrary Noise}, author = {Montagna, Francesco and Noceti, Nicoletta and Rosasco, Lorenzo and Zhang, Kun and Locatello, Francesco}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {726--751}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/montagna23a/montagna23a.pdf}, url = {https://proceedings.mlr.press/v213/montagna23a.html}, abstract = {Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.} }
Endnote
%0 Conference Paper %T Causal Discovery with Score Matching on Additive Models with Arbitrary Noise %A Francesco Montagna %A Nicoletta Noceti %A Lorenzo Rosasco %A Kun Zhang %A Francesco Locatello %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-montagna23a %I PMLR %P 726--751 %U https://proceedings.mlr.press/v213/montagna23a.html %V 213 %X Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.
APA
Montagna, F., Noceti, N., Rosasco, L., Zhang, K. & Locatello, F.. (2023). Causal Discovery with Score Matching on Additive Models with Arbitrary Noise. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:726-751 Available from https://proceedings.mlr.press/v213/montagna23a.html.

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