Learning Deep Kernels for Non-Parametric Independence Testing
The Hilbert-Schmidt Independence Criterion (HSIC) is a powerful tool for nonparametric detection of dependence between random variables. It crucially depends, however, on the selection of reasonable kernels; commonly-used choices like the Gaussian kernel, or the kernel that yields the distance covariance, are sufficient only for amply sized samples from data distributions with relatively simple forms of dependence. We propose a scheme for selecting the kernels used in an HSIC-based independence test, based on maximizing an estimate of the asymptotic test power. We prove that maximizing this estimate indeed approximately maximizes the true power of the test, and demonstrate that our learned kernels can identify forms of structured dependence between random variables in various experiments.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing
To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenome…
Equivalence of distance-based and RKHS-based statistics in hypothesis testing
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, …
Two-sample testingOn the Decreasing Power of Kernel and Distance based Nonparametric Hypothesis Tests in High Dimensions
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs…
Two-sample testingLearning Interpretable Characteristic Kernels via Decision Forests
Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are indu…
Feature ImportanceGeneral ClassificationA Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment
Causal inference grows increasingly complex as the number of confounders increases. Given treatments $X$, confounders $Z$ and outcomes $Y$, we develop a non-parametric method to test the \textit{do-null} hypothesis $H_0:…
Causal Inference