Search Machine Learning Repository: Quantile Regression for Large-scale Applications
Authors: Jiyan Yang, Xiangrui Meng and Michael Mahoney
Conference: Proceedings of the 30th International Conference on Machine Learning (ICML-13)
Year: 2013
Pages: 881-887
Abstract: Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, \emph{e.g.}, involving data up to and beyond the terabyte regime, remains a challenge. Here, we present a randomized algorithm that runs in time that is nearly linear in the size of the input and that, with constant probability, computes a $(1+\epsilon)$ approximate solution to an arbitrary quantile regression problem. Our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that it can be implemented in MapReduce-like environments and applied to terabyte-sized problems.
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