Background: Identifying molecular signatures of disease phenotypes is studied using two mainstream approaches:\n(i) Predictive modeling methods such as linear classification and regression algorithms are used to find signatures\npredictive of phenotypes from genomic data, which may not be robust due to limited sample size or highly correlated\nnature of genomic data. (ii) Gene set analysis methods are used to find gene sets on which phenotypes are linearly\ndependent by bringing prior biological knowledge into the analysis, which may not capture more complex nonlinear\ndependencies. Thus, formulating an integrated model of gene set analysis and nonlinear predictive modeling is of\ngreat practical importance.\nResults: In this study, we propose a Bayesian binary classification framework to integrate gene set analysis and\nnonlinear predictive modeling. We then generalize this formulation to multitask learning setting to model multiple\nrelated datasets conjointly. Our main novelty is the probabilistic nonlinear formulation that enables us to robustly\ncapture nonlinear dependencies between genomic data and phenotype even with small sample sizes. We\ndemonstrate the performance of our algorithms using repeated random subsampling validation experiments on two\ncancer and two tuberculosis datasets by predicting important disease phenotypes from genome-wide gene\nexpression data.\nConclusions: We are able to obtain comparable or even better predictive performance than a baseline Bayesian\nnonlinear algorithm and to identify sparse sets of relevant genes and gene sets on all datasets. We also show that our\nmultitask learning formulation enables us to further improve the generalization performance and to better\nunderstand biological processes behind disease phenotypes.
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