Conditional independence testing under misspecified inductive biases

被引:0
|
作者
Polo, Felipe Maia [1 ]
Sun, Yuekai [1 ]
Banerjee, Moulinath [1 ]
机构
[1] Univ Michigan, Dept Stat, Ann Arbor, MI 48109 USA
来源
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 36 (NEURIPS 2023) | 2023年
基金
美国国家科学基金会;
关键词
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes predictors as an intermediate step; we refer to this class of tests as regression-based tests. Although these methods are guaranteed to control Type-I error when the supervised learning methods accurately estimate the regression functions or Bayes predictors of interest, their behavior is less understood when they fail due to misspecified inductive biases; in other words, when the employed models are not flexible enough or when the training algorithm does not induce the desired predictors. Then, we study the performance of regression-based CI tests under misspecified inductive biases. Namely, we propose new approximations or upper bounds for the testing errors of three regression-based tests that depend on misspecification errors. Moreover, we introduce the Rao-Blackwellized Predictor Test (RBPT), a regression-based CI test robust against misspecified inductive biases. Finally, we conduct experiments with artificial and real data, showcasing the usefulness of our theory and methods.
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页数:36
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