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Title: Conquer: Convolution-smoothed quantile regression Authors:  Wenxin Zhou - University of California San Diego (United States) [presenting]
Kean Ming Tan - University of Michigan (United States)
Lan Wang - University of Minnesota (United States)
Abstract: Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. We discuss a convolution-smoothed approach for quantile regression, which is particularly suited for large-scale problems in both ``increasing dimension'' and ``high-dimensional'' regimes. This method, which we refer to as conquer, turns the non-differentiable check loss into a twice-differentiable, convex, and locally strongly convex surrogate, and therefore admits fast and scalable gradient-based algorithms to perform optimization.