1Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), University Medical Center, 55131 Mainz, Germany2Department of Internal Medicine III, University Hospital of Ulm, 89081 Ulm, Germany3Institute for Medical Biometry and Statistics, Faculty of Medicine and Medical Center - University of Freiburg, 79104 Freiburg, Germany
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MotivationLearning the joint distributions of measurements, and in particular identification of an appropriate low-dimensional manifold, has been found to be a powerful ingredient of deep leaning approaches. Yet, such approaches have hardly been applied to single nucleotide polymorphism (SNP) data, probably due to the high number of features typically exceeding the number of studied individuals.ResultsAfter a brief overview of how deep Boltzmann machines (DBMs), a deep learning approach, can be adapted to SNP data in principle, we specifically present a way to alleviate the dimensionality problem by partitioned learning. We propose a sparse regression approach to coarsely screen the joint distribution of SNPs, followed by training several DBMs on SNP partitions that were identified by the screening. Aggregate features representing SNP patterns and the corresponding SNPs are extracted from the DBMs by a combination of statistical tests and sparse regression. In simulated case-control data, we show how this can uncover complex SNP patterns and augment results from univariate approaches, while maintaining type 1 error control. Time-to-event endpoints are considered in an application with acute myeloid leukemia patients, where SNP patterns are modeled after a pre-screening based on gene expression data. The proposed approach identified three SNPs that seem to jointly influence survival in a validation dataset. This indicates the added value of jointly investigating SNPs compared to standard univariate analyses and makes partitioned learning of DBMs an interesting complementary approach when analyzing SNP data.Availability and implementationA Julia package is provided at ‘http://github.com/binderh/BoltzmannMachines.jl’.Contactbinderh@imbi.uni-freiburg.deSupplementary informationSupplementary data are available at Bioinformatics online.