Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decomposition
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914685239951360 |
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| author | Dong, Shuyu Uemura, Kento Fujii, Akito Chang, Shuang Koyanagi, Yusuke Maruhashi, Koji Sebag, Michèle |
| author_facet | Dong, Shuyu Uemura, Kento Fujii, Akito Chang, Shuang Koyanagi, Yusuke Maruhashi, Koji Sebag, Michèle |
| contents | Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on learning causal structures from the inverse covariance matrix. The proposed method, called ICID for Independence-preserving Decomposition from Inverse Covariance matrix, is based on continuous optimization of a matrix decomposition model that preserves the nonzero patterns of the inverse covariance matrix. Through theoretical and empirical evidences, we show that ICID efficiently identifies the sought directed acyclic graph (DAG) assuming the knowledge of noise variances. Moreover, ICID is shown empirically to be robust under bounded misspecification of noise variances in the case where the noise variances are non-equal. The proposed method enjoys a low complexity, as reflected by its time efficiency in the experiments, and also enables a novel regularization scheme that yields highly accurate solutions on the Simulated fMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14221 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decomposition Dong, Shuyu Uemura, Kento Fujii, Akito Chang, Shuang Koyanagi, Yusuke Maruhashi, Koji Sebag, Michèle Machine Learning Optimization and Control Methodology Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on learning causal structures from the inverse covariance matrix. The proposed method, called ICID for Independence-preserving Decomposition from Inverse Covariance matrix, is based on continuous optimization of a matrix decomposition model that preserves the nonzero patterns of the inverse covariance matrix. Through theoretical and empirical evidences, we show that ICID efficiently identifies the sought directed acyclic graph (DAG) assuming the knowledge of noise variances. Moreover, ICID is shown empirically to be robust under bounded misspecification of noise variances in the case where the noise variances are non-equal. The proposed method enjoys a low complexity, as reflected by its time efficiency in the experiments, and also enables a novel regularization scheme that yields highly accurate solutions on the Simulated fMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms. |
| title | Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decomposition |
| topic | Machine Learning Optimization and Control Methodology |
| url | https://arxiv.org/abs/2211.14221 |