A method for learning a sparse classifier in the presence of missing data for high-dimensional biological datasets

Motivation: This work addresses two common issues in building classification models for biological or medical studies: learning a sparse model, where only a subset of a large number of possible predictors is used, and training in the presence of missing data. This work focuses on supervised generative binary classification models, specifically linear discriminant analysis (LDA). The parameters are determined using an expectation maximization algorithm to both address missing data and introduce priors to promote sparsity. The proposed algorithm, expectationmaximization sparse discriminant analysis (EM-SDA), produces a sparse LDA model for datasets with and without missing data. Results: EM-SDA is tested via simulations and case studies. In the simulations, EM-SDA is compared with nearest shrunken centroids (NSCs) and sparse discriminant analysis (SDA) with k-nearest neighbors for imputation for varying mechanism and amount of missing data. In three case studies using published biomedical data, the results are compared with NSC and SDA models with four different types of imputation, all of which are common approaches in the field. EM-SDA is more accurate and sparse than competing methods both with and without missing data in most of the experiments. Furthermore, the EM-SDA results are mostly consistent between the missing and full cases. Biological relevance of the resulting models, as quantified via a literature search, is also presented. Availability and implementation: A Matlab implementation published under GNU GPL v.3 license is available at http://web.mit.edu/braatzgroup/links.html.