High-Dimensional Structured Quantile Regression

Vidyashankar Sivakumar, Arindam Banerjee
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3220-3229, 2017.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-sivakumar17a, title = {High-Dimensional Structured Quantile Regression}, author = {Vidyashankar Sivakumar and Arindam Banerjee}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3220--3229}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/sivakumar17a/sivakumar17a.pdf}, url = {https://proceedings.mlr.press/v70/sivakumar17a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T High-Dimensional Structured Quantile Regression %A Vidyashankar Sivakumar %A Arindam Banerjee %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-sivakumar17a %I PMLR %P 3220--3229 %U https://proceedings.mlr.press/v70/sivakumar17a.html %V 70 %X 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.
APA
Sivakumar, V. & Banerjee, A.. (2017). High-Dimensional Structured Quantile Regression. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3220-3229 Available from https://proceedings.mlr.press/v70/sivakumar17a.html.

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