Robust differential expression analysis by learning discriminant boundary in multi-dimensional space of statistical attributes

Yuanzhe Bei, Pengyu Hong

Performing statistical tests is an important step in analyzing genome-wide datasets for detecting genomic features differentially expressed between conditions. Each type of statistical test has its own advantages in characterizing certain aspects of differences between population means and often assumes a relatively simple data distribution (e.g., Gaussian, Poisson, negative binomial, etc.), which may not be well met by the datasets of interest. Making insufficient distributional assumptions can lead to inferior results when dealing with complex differential expression patterns. We propose to capture differential expression information more comprehensively by integrating multiple test statistics, each of which has relatively limited capacity to summarize the observed differential expression information. This work addresses a general application scenario, in which users want to detect as many as DEFs while requiring the false discovery rate (FDR) to be lower than a cut-off. We treat each test statistic as a basic attribute, and model the detection of differentially expressed genomic features as learning a discriminant boundary in a multi-dimensional space of basic attributes. We mathematically formulated our goal as a constrained optimization problem aiming to maximize discoveries satisfying a user-defined FDR. An effective algorithm, Discriminant-Cut, has been developed to solve an instantiation of this problem. Extensive comparisons of Discriminant-Cut with 13 existing methods were carried out to demonstrate its robustness and effectiveness. We have developed a novel machine learning methodology for robust differential expression analysis, which can be a new avenue to significantly advance research on large-scale differential expression analysis.