Estimation rates for sparse linear cyclic causal models
© Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020. All rights reserved. Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population-or infi...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/1721.1/137028 |
| _version_ | 1826190116706582528 |
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| author | Hütter, JC Rigollet, P |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hütter, JC Rigollet, P |
| author_sort | Hütter, JC |
| collection | MIT |
| description | © Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020. All rights reserved. Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population-or infinite-sample-case, where distributions are assumed to be known, little is known about the statistical rates of convergence of various methods, even for the simplest models. In this work, allowing for cycles, we study linear structural equations models with homoscedastic Gaussian noise and in the presence of interventions that make the model identifiable. More specifically, we present statistical rates of estimation for both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments. |
| first_indexed | 2024-09-23T08:35:17Z |
| format | Article |
| id | mit-1721.1/137028 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:35:17Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1370282023-02-09T19:57:36Z Estimation rates for sparse linear cyclic causal models Hütter, JC Rigollet, P Massachusetts Institute of Technology. Department of Mathematics © Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020. All rights reserved. Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population-or infinite-sample-case, where distributions are assumed to be known, little is known about the statistical rates of convergence of various methods, even for the simplest models. In this work, allowing for cycles, we study linear structural equations models with homoscedastic Gaussian noise and in the presence of interventions that make the model identifiable. More specifically, we present statistical rates of estimation for both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments. 2021-11-01T18:25:46Z 2021-11-01T18:25:46Z 2020 2021-05-26T13:43:14Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137028 Hütter, JC and Rigollet, P. 2020. "Estimation rates for sparse linear cyclic causal models." Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020. en http://proceedings.mlr.press/v124/huetter20a.html Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Proceedings of Machine Learning Research |
| spellingShingle | Hütter, JC Rigollet, P Estimation rates for sparse linear cyclic causal models |
| title | Estimation rates for sparse linear cyclic causal models |
| title_full | Estimation rates for sparse linear cyclic causal models |
| title_fullStr | Estimation rates for sparse linear cyclic causal models |
| title_full_unstemmed | Estimation rates for sparse linear cyclic causal models |
| title_short | Estimation rates for sparse linear cyclic causal models |
| title_sort | estimation rates for sparse linear cyclic causal models |
| url | https://hdl.handle.net/1721.1/137028 |
| work_keys_str_mv | AT hutterjc estimationratesforsparselinearcycliccausalmodels AT rigolletp estimationratesforsparselinearcycliccausalmodels |