Doubly robust and computationally efficient high-dimensional variable selection
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911252305936384 |
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| author | Chakraborty, Abhinav Zhang, Jeffrey Katsevich, Eugene |
| author_facet | Chakraborty, Abhinav Zhang, Jeffrey Katsevich, Eugene |
| contents | Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing $p$ variables requires $O(p)$ fits. Inspired by model-X ideas, we observe that an estimate of the joint predictor distribution and a single response-on-all-predictors fit can be used to reconstruct all PCM fits. This yields tower PCM (tPCM), a computationally efficient extension of PCM to variable selection. When the joint predictor distribution is sufficiently tractable, as in applications like genome-wide association studies, tPCM offers a substantial speedup over PCM -- up to 130$\times$ in our simulations -- while matching its power. tPCM also improves on model-X methods like knockoffs and holdout randomization test (HRT) by returning per-variable $p$-values and improving speed, respectively. We prove that tPCM is doubly robust and asymptotically equivalent to both PCM and HRT. We thus extend the bridge between model-X and doubly robust approaches, demonstrating their independent arrival at equivalent methods and showing that this intersection is a fruitful source of new methodologies like tPCM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Doubly robust and computationally efficient high-dimensional variable selection Chakraborty, Abhinav Zhang, Jeffrey Katsevich, Eugene Methodology Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing $p$ variables requires $O(p)$ fits. Inspired by model-X ideas, we observe that an estimate of the joint predictor distribution and a single response-on-all-predictors fit can be used to reconstruct all PCM fits. This yields tower PCM (tPCM), a computationally efficient extension of PCM to variable selection. When the joint predictor distribution is sufficiently tractable, as in applications like genome-wide association studies, tPCM offers a substantial speedup over PCM -- up to 130$\times$ in our simulations -- while matching its power. tPCM also improves on model-X methods like knockoffs and holdout randomization test (HRT) by returning per-variable $p$-values and improving speed, respectively. We prove that tPCM is doubly robust and asymptotically equivalent to both PCM and HRT. We thus extend the bridge between model-X and doubly robust approaches, demonstrating their independent arrival at equivalent methods and showing that this intersection is a fruitful source of new methodologies like tPCM. |
| title | Doubly robust and computationally efficient high-dimensional variable selection |
| topic | Methodology |
| url | https://arxiv.org/abs/2409.09512 |