A kernel test for causal association via noise contrastive backdoor adjustment
Causal inference grows increasingly complex as the dimension of confounders increases. Given treatments X𝑋, outcomes Y𝑌, and measured confounders Z𝑍, we develop a non-parametric method to test the do-null hypothesis that, after an intervention on X𝑋, there is no marginal dependence of Y𝑌 on X𝑋, agai...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Journal of Machine Learning Research
2024
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| _version_ | 1826313913881329664 |
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| author | Hu, R Sejdinovic, D Evans, RJ |
| author_facet | Hu, R Sejdinovic, D Evans, RJ |
| author_sort | Hu, R |
| collection | OXFORD |
| description | Causal inference grows increasingly complex as the dimension of confounders increases. Given treatments X𝑋, outcomes Y𝑌, and measured confounders Z𝑍, we develop a non-parametric method to test the do-null hypothesis that, after an intervention on X𝑋, there is no marginal dependence of Y𝑌 on X𝑋, against the general alternative. Building on the Hilbert-Schmidt Independence Criterion (HSIC) for marginal independence testing, we propose backdoor-HSIC (bd-HSIC), an importance weighted HSIC which combines density ratio estimation with kernel methods. Experiments on simulated data verify the correct size and that the estimator has power for both binary and continuous treatments under a large number of confounding variables. Additionally, we establish convergence properties of the estimators of covariance operators used in bd-HSIC. We investigate the advantages and disadvantages of bd-HSIC against parametric tests as well as the importance of using the do-null testing in contrast to marginal or conditional independence testing. A complete implementation can be found at https://github.com/MrHuff/kgformula. |
| first_indexed | 2024-09-25T04:23:54Z |
| format | Journal article |
| id | oxford-uuid:a0e08ac1-d7f8-4d3f-98b8-254a50157dc4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:23:54Z |
| publishDate | 2024 |
| publisher | Journal of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:a0e08ac1-d7f8-4d3f-98b8-254a50157dc42024-08-19T15:19:40ZA kernel test for causal association via noise contrastive backdoor adjustmentJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a0e08ac1-d7f8-4d3f-98b8-254a50157dc4EnglishSymplectic ElementsJournal of Machine Learning Research2024Hu, RSejdinovic, DEvans, RJCausal inference grows increasingly complex as the dimension of confounders increases. Given treatments X𝑋, outcomes Y𝑌, and measured confounders Z𝑍, we develop a non-parametric method to test the do-null hypothesis that, after an intervention on X𝑋, there is no marginal dependence of Y𝑌 on X𝑋, against the general alternative. Building on the Hilbert-Schmidt Independence Criterion (HSIC) for marginal independence testing, we propose backdoor-HSIC (bd-HSIC), an importance weighted HSIC which combines density ratio estimation with kernel methods. Experiments on simulated data verify the correct size and that the estimator has power for both binary and continuous treatments under a large number of confounding variables. Additionally, we establish convergence properties of the estimators of covariance operators used in bd-HSIC. We investigate the advantages and disadvantages of bd-HSIC against parametric tests as well as the importance of using the do-null testing in contrast to marginal or conditional independence testing. A complete implementation can be found at https://github.com/MrHuff/kgformula. |
| spellingShingle | Hu, R Sejdinovic, D Evans, RJ A kernel test for causal association via noise contrastive backdoor adjustment |
| title | A kernel test for causal association via noise contrastive backdoor adjustment |
| title_full | A kernel test for causal association via noise contrastive backdoor adjustment |
| title_fullStr | A kernel test for causal association via noise contrastive backdoor adjustment |
| title_full_unstemmed | A kernel test for causal association via noise contrastive backdoor adjustment |
| title_short | A kernel test for causal association via noise contrastive backdoor adjustment |
| title_sort | kernel test for causal association via noise contrastive backdoor adjustment |
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