730
Views
3
CrossRef citations to date
0
Altmetric
Theory and Methods

Anytime-Valid Tests of Conditional Independence Under Model-X

ORCID Icon, &
Pages 1554-1565 | Received 21 Oct 2022, Accepted 13 Apr 2023, Published online: 05 Jun 2023

References

  • Azadkia, M., Chatterjee, S. (2021), “A Simple Measure of Conditional Dependence,” The Annals of Statistics, 49, 3070–3102. DOI: 10.1214/21-AOS2073.
  • Barron, A. (1998), “Information-Theoretic Characterization of Bayes Performance and the Choice of Priors in Parametric and Nonparametric Problems,” in Bayesian Statistics (Vol. 6), eds. Bernardo, J. M., Berger, J. O., Dawid, A. P., Smith, A. F. M., pp. 27–52, Oxford: Oxford University Press.
  • Berrett, T. B., Wang, Y., Barber, R. F., and Samworth, R. J. (2020), “The Conditional Permutation Test for Independence While Controlling for Confounders,” Journal of the Royal Statistical Society, Series B, 82, 175–197. DOI: 10.1111/rssb.12340.
  • Bilodeau, B., Foster, D. J., and Roy, D. M. (2021), “Minimax Rates for Conditional Density Estimation via Empirical Entropy,” arXiv preprint arXiv:2109.10461.
  • Candès, E., Fan, Y., Janson, L., and Lv, J. (2018), “Panning for Gold: ‘Model-X’ Knockoffs for High Dimensional Controlled Variable Selection,” Journal of the Royal Statistical Society, Series B, 80, 551–577. DOI: 10.1111/rssb.12265.
  • Casper, C., Cook, T., and on FORTRAN program ld98., O. A. P. B. (2022), ldbounds: Lan-DeMets Method for Group Sequential Boundaries, R package version 2.0.0.
  • Cover, T. M., and Thomas, J. A. (1991), Elements of Information Theory, Wiley Series in Telecommunications, New York: Wiley.
  • Darling, D., and Robbins, H. (1967), “Confidence Sequences for Mean, Variance, and Median,” Proceedings of the National Academy of Sciences, 58, 66–68. DOI: 10.1073/pnas.58.1.66.
  • Dawid, A. P. (1979), “Conditional Independence in Statistical Theory,” Journal of the Royal Statistical Society, Series B, 41, 1–15. DOI: 10.1111/j.2517-6161.1979.tb01052.x.
  • Duan, B., Ramdas, A., and Wasserman, L. (2022), “Interactive Rank Testing by Betting,” in Proceedings of the First Conference on Causal Learning and Reasoning, Vol. 177 of Proceedings of Machine Learning Research, pp. 201–235.
  • Foster, D. J., Kale, S., Luo, H., Mohri, M., and Sridharan, K. (2018), “Logistic Regression: The Importance of Being Improper,” in Proceedings COLT, pp. 167–208.
  • Fukumizu, K., Gretton, A., Sun, X., and Schölkopf, B. (2007), “Kernel Measures of Conditional Dependence,” in Advances in Neural Information Processing Systems (Vol. 20).
  • Grünwald, P. (2022), “Beyond Neyman-Pearson,” arXiv preprint arXiv: 2205.00901.
  • Grünwald, P. D., and Mehta, N. A. (2020), “Fast Rates for General Unbounded Loss Functions,” Journal of Machine Learning Research, 21, 1–80.
  • Grünwald, P., de Heide, R., and Koolen, W. (2019), “Safe Testing,” arXiv preprint arXiv:1906.07801.
  • Ham, D. W., Imai, K., and Janson, L. (2022), “Using Machine Learning to Test Causal Hypotheses in Conjoint Analysis,” arXiv preprint arXiv:2201.08343.
  • Katsevich, E., and Ramdas, A. (2022), “On the Power of Conditional Independence Testing Under Model-X,” Electronic Journal of Statistics, 16, 6348–6394. DOI: 10.1214/22-EJS2085.
  • Koolen, W. M., and Grünwald, P. (2022), “Log-Optimal Anytime-Valid E-Values,” International Journal of Approximate Reasoning, 141, 69–82. DOI: 10.1016/j.ijar.2021.09.010.
  • Li, S., and Liu, M. (2022), “Maxway CRT: Improving the Robustness of Model-X Inference,” arXiv preprint arXiv:2203.06496.
  • Liu, M., Katsevich, E., Janson, L., and Ramdas, A. (2021), “Fast and Powerful Conditional Randomization Testing via Distillation,” Biometrika, 109, 277–293. DOI: 10.1093/biomet/asab039.
  • McCullagh, P., and Nelder, J. (1989), Generalized Linear Models (2nd ed.), CRC Monographs on Statistics and Applied Probability Series, New York: Chapman & Hall.
  • Niu, Z., Chakraborty, A., Dukes, O., Katsevich, E., (2022), “Reconciling Model-X and Doubly Robust Approaches to Conditional Independence Testing,” arXiv preprint arXiv:2211.14698.
  • O’Brien, P. C., and Fleming, T. R. (1979), “A Multiple Testing Procedure for Clinical Trials,” Biometrics, 35, 549–556.
  • Pocock, S. J. (1977), “Group Sequential Methods in the Design and Analysis of Clinical Trials,” Biometrika, 64, 191–199. DOI: 10.1093/biomet/64.2.191.
  • Pocock, S. J., and Simon, R. (1975), “Sequential Treatment Assignment with Balancing for Prognostic Factors in the Controlled Clinical Trial,” Biometrics, 31, 103–115.
  • Qian, G., and Field, C. (2002), “Law of Iterated Logarithm and Consistent Model Selection Criterion in Logistic Regression,” Statistics & Probability Letters, 56, 101–112. DOI: 10.1016/S0167-7152(01)00191-2.
  • R Core Team (2022), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Ramdas, A., Ruf, J., Larsson, M., and Koolen, W. (2020), “Admissible Anytime-Valid Sequential Inference Must Rely on Nonnegative Martingales,” arXiv preprint arXiv:2009.03167.
  • Ramdas, A., Ruf, J., Larsson, M., and Koolen, W. M. (2022), “Testing Exchangeability: Fork-Convexity, Supermartingales and E-Processes,” International Journal of Approximate Reasoning, 141, 83–109. DOI: 10.1016/j.ijar.2021.06.017.
  • Robbins, H. (1952), “Some Aspects of the Sequential Design of Experiments,” Bulletin of the American Mathematical Society, 58, 527–535. DOI: 10.1090/S0002-9904-1952-09620-8.
  • Runge, J. (2018), “Conditional Independence Testing Based on a Nearest-Neighbor Estimator of Conditional Mutual Information,” in Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (Vol. 84) of Proceedings of Machine Learning Research, pp. 938–947.
  • Shaer, S., Maman, G., and Romano, Y. (2022), “Model-Free Sequential Testing for Conditional Independence via Testing by Betting,” arXiv preprint arXiv:2210.00354.
  • Shafer, G. (2021), “Testing by Betting: A Strategy for Statistical and Scientific Communication,” Journal of the Royal Statistical Society, Series A, 184, 407–431. DOI: 10.1111/rssa.12647.
  • Shah, R. D., and Peters, J. (2020), “The Hardness of Conditional Independence Testing and the Generalized Covariance Measure,” The Annals of Statistics, 48, 1514–1538. DOI: 10.1214/19-AOS1857.
  • Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2011), “Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent,” Journal of Statistical Software, 39, 1–13. DOI: 10.18637/jss.v039.i05.
  • Ter Schure, J., Perez-Ortiz, M. F., Ly, A., and Grunwald, P. (2020), “The Safe Logrank Test: Error Control under Continuous Monitoring with Unlimited Horizon,” arXiv preprint arXiv:2011.06931.
  • Turner, R., Ly, A., and Grünwald, P. (2021), “Generic E-Variables for Exact Sequential k-Sample Tests That Allow for Optional Stopping,” arXiv preprint arXiv:2106.02693.
  • Vovk, V., and Wang, R. (2021), “E-values: Calibration, Combination and Applications,” The Annals of Statistics, 49, 1736–1754. DOI: 10.1214/20-AOS2020.
  • Wald, A. (1947), Sequential Analysis, New York: Wiley.
  • Wasserman, L., Ramdas, A., and Balakrishnan, S. (2020), “Universal Inference,” Proceedings of the National Academy of Sciences, 117, 16880–16890. DOI: 10.1073/pnas.1922664117.
  • Wong, W. H., and Shen, X. S. (1995), “Probability Inequalities for Likelihood Ratios and Convergence Rates of Sieve MLES,” The Annals of Statistics, 23, 339–362. DOI: 10.1214/aos/1176324524.
  • Zhang, L.-X., Hu, F., Cheung, S. H., and Chan, W. S. (2007), “Asymptotic Properties of Covariate-Adjusted Response-Adaptive Designs,” The Annals of Statistics, 35, 1166–1182. DOI: 10.1214/009053606000001424.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.