Multiple Testing under Dependence via Semiparametric Graphical Models
The 31st International Conference on Machine Learning (ICML), 2014 .

Jie Liu, Chunming Zhang, Elizabeth Burnside, and David Page.

  • Abstract: It has been shown that graphical models can be used to leverage the dependence in large-scale multiple testing problems with significantly improved performance (Sun & Cai, 2009; Liu et al., 2012). These graphical models are fully parametric and require that we know the parameterization of f_1 --- the density function of the test statistic under the alternative hypothesis. However in practice, f_1 is often heterogeneous, and cannot be estimated with a simple parametric distribution. We propose a novel semiparametric approach for multiple testing under dependence, which estimates f_1 adaptively. This semiparametric approach exactly generalizes the local FDR procedure (Efron et al., 2001) and connects with the BH procedure (Benjamini & Hochberg, 1995). A variety of simulations show that our semiparametric approach outperforms classical procedures which assume independence and the parametric approaches which capture dependence.

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