  Conventional multiple testing procedures often assume hypotheses for
different features are exchangeable. However, in many scientific applications,
additional covariate information regarding the patterns of signals and nulls
are available. In this paper, we introduce an FDR control procedure in
large-scale inference problem that can incorporate covariate information. We
develop a fast algorithm to implement the proposed procedure and prove its
asymptotic validity even when the underlying model is misspecified and the
p-values are weakly dependent (e.g., strong mixing). Extensive simulations are
conducted to study the finite sample performance of the proposed method and we
demonstrate that the new approach improves over the state-of-the-art approaches
by being flexible, robust, powerful and computationally efficient. We finally
apply the method to several omics datasets arising from genomics studies with
the aim to identify omics features associated with some clinical and biological
phenotypes. We show that the method is overall the most powerful among
competing methods, especially when the signal is sparse. The proposed Covariate
Adaptive Multiple Testing procedure is implemented in the R package CAMT.
