Abstract:
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Analysis of high-dimensional, under-sampled data has become increasingly important in Genomics with its expanding repertoire of high-throughput technologies. For many regression-like analyses, dimension reduction in the predictor space can be very effective. The most commonly used approaches assume that predictors and samples are similar in nature and can simultaneously participate in the reduction. However, recent high-throughput genomic data is often heterogeneous and structured. Exploiting known structure in samples and predictors when performing dimension reduction can be an avenue for integrating data collected through multiple studies and diverse high-throughput platforms. To address this challenge, we propose a new Sufficient Dimension Reduction (SDR) approach; Structured Ordinary Least Squares (sOLS). sOLS combines ideas from existing SDR literature to merge reductions performed within subgroups of samples and/or predictors. As a part of our proposal, we developed group-wise OLS (gOLS) to efficiently perform SDR for grouped predictors. Simulation studies and a first application to ENCODE genomic data show promising performance for our methodology.
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