Journal article
Testing conditional independence in supervised learning algorithms
- Abstract:
- We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of Candès et al. (J R Stat Soc Ser B 80:551–577, 2018), we develop a novel testing procedure that works in conjunction with any valid knockoff sampler, supervised learning algorithm, and loss function. The CPI can be efficiently computed for high-dimensional data without any sparsity constraints. We demonstrate convergence criteria for the CPI and develop statistical inference procedures for evaluating its magnitude, significance, and precision. These tests aid in feature and model selection, extending traditional frequentist and Bayesian techniques to general supervised learning tasks. The CPI may also be applied in causal discovery to identify underlying multivariate graph structures. We test our method using various algorithms, including linear regression, neural networks, random forests, and support vector machines. Empirical results show that the CPI compares favorably to alternative variable importance measures and other nonparametric tests of conditional independence on a diverse array of real and synthetic datasets. Simulations confirm that our inference procedures successfully control Type I error with competitive power in a range of settings. Our method has been implemented in an R package, cpi, which can be downloaded from https://github.com/dswatson/cpi.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 2.1MB, Terms of use)
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(Supplementary materials, doc, 3.7MB, Terms of use)
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- Publisher copy:
- 10.1007/s10994-021-06030-6
Authors
- Publisher:
- Springer
- Journal:
- Machine Learning More from this journal
- Volume:
- 110
- Issue:
- 8
- Pages:
- 2107–2129
- Publication date:
- 2021-08-02
- Acceptance date:
- 2021-06-16
- DOI:
- EISSN:
-
1573-0565
- ISSN:
-
0885-6125
- Language:
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English
- Keywords:
- Pubs id:
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968967
- Local pid:
-
pubs:968967
- Deposit date:
-
2020-02-04
Terms of use
- Copyright holder:
- Watson and Wright
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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