Peel learning for pathway-related outcome prediction

Abstract Motivation Traditional regression models are limited in outcome prediction due to their parametric nature. Current deep learning methods allow for various effects and interactions and have shown improved performance, but they typically need to be trained on a large amount of data to obtain reliable results. Gene expression studies often have small sample sizes but high dimensional correlated predictors so that traditional deep learning methods are not readily applicable. Results In this article, we proposed peel learning, a novel neural network that incorporates the prior relationship among genes. In each layer of learning, overall structure is peeled into multiple local substructures. Within the substructure, dependency among variables is reduced through linear projections. The overall structure is gradually simplified over layers and weight parameters are optimized through a revised backpropagation. We applied PL to a small lung transplantation study to predict recipients’ post-surgery primary graft dysfunction using donors’ gene expressions within several immunology pathways, where PL showed improved prediction accuracy compared to conventional penalized regression, classification trees, feed-forward neural network and a neural network assuming prior network structure. Through simulation studies, we also demonstrated the advantage of adding specific structure among predictor variables in neural network, over no or uniform group structure, which is more favorable in smaller studies. The empirical evidence is consistent with our theoretical proof of improved upper bound of PL’s complexity over ordinary neural networks. Availability and implementation PL algorithm was implemented in Python and the open-source code and instruction will be available at https://github.com/Likelyt/Peel-Learning. Supplementary information Supplementary data are available at Bioinformatics online.