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High-Dimensional Structured Quantile Regression
Vidyashankar Sivakumar · Arindam Banerjee

Tue Aug 08 06:06 PM -- 06:24 PM (PDT) @ C4.4
in High dimensional estimation »

Quantile regression aims at modeling the conditional median and quantiles of a response variable given certain predictor variables. In this work we consider the problem of linear quantile regression in high dimensions where the number of predictor variables is much higher than the number of samples available for parameter estimation. We assume the true parameter to have some structure characterized as having a small value according to some atomic norm R(.) and consider the norm regularized quantile regression estimator. We characterize the sample complexity for consistent recovery and give non-asymptotic bounds on the estimation error. While this problem has been previously considered, our analysis reveals geometric and statistical characteristics of the problem not available in prior literature. We perform experiments on synthetic data which support the theoretical results.

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Author Information

Vidyashankar Sivakumar (University of Minnesota)
Arindam Banerjee (University of Minnesota)
Arindam Banerjee

Arindam Banerjee is a Founder Professor at the Department of Computer Science, University of Illinois Urbana-Champaign. His research interests are in machine learning. His current research focuses on computational and statistical aspects of over-parameterized models including deep learning, spatial and temporal data analysis, generative models, and sequential decision making problems. His work also focuses on applications of machine learning in complex real-world and scientific domains including problems in climate science and ecology. He has won several awards, including the NSF CAREER award, the IBM Faculty Award, and six best paper awards in top-tier venues.

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