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Title: A fast adaptive algorithm for quantile regression with shared design matrix Authors:  Ying Wei - Columbia University (United States) [presenting]
Ethan Fang - Penn Stat University (United States)
Tianchen Xu - Columbia University (United States)
Abstract: Quantile regression is an important modeling tool that provides a complete picture of associations among a response variable $Y$ and its covariates $\Xb$. Due to its flexibility, quantile regression has become a popular alternative to least squares regression for modeling heterogeneous data, especially in high dimensional datasets. Though there are several estimating algorithms, in the procedure of variable selection of a high dimensional dataset, we still confront a challenge that fitting a large number of quantile regressions is often time consuming. We notice that, in many large scale genetic studies, the design matrices often share a considerable similarity among these regressions. Such a fact motivates us to develop an adaptive algorithm that could utilize the information from analogous regressions, and boost up the whole fitting procedure. The developed new algorithms was applied to eQTL analysis using GTEx data, and resulted in significant reduction of computing time.