Transfer Learning in Multiple Hypothesis Testing.

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test many hypotheses using the same family of sampling parametric models. A two-step methodology is employed: initially, a learning phase is conducted utilizing simulated datasets encompassing a wide spectrum of null and alternative hypotheses, followed by a transfer phase applying this fitted model to real-world experimental sequences. The outcome is a CNN model capable of navigating the complex domain of MHT with improved precision over traditional methods, also demonstrating robustness under varying conditions, including the number of true nulls and dependencies between tests. Although indications of empirical evaluations are presented and show that the methodology will prove useful, more work is required to provide a full evaluation from a theoretical perspective. The potential of this innovative approach is further illustrated within the critical domain of genomics. Although formal proof of the consistency of the model remains elusive due to the inherent complexity of the algorithms, this paper also provides some theoretical insights and advocates for continued exploration of this methodology.

Large scale maximum average power multiple inference on time-course count data with application to RNA-seq analysis.

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.