%0 Conference Paper %1 pmlr-v70-sivakumar17a %A Sivakumar, Vidyashankar %A Banerjee, Arindam %B Proceedings of the 34th International Conference on Machine Learning %D 2017 %E Precup, Doina %E Teh, Yee Whye %I PMLR %K todo:neurips %P 3220--3229 %T High-Dimensional Structured Quantile Regression %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.

@inproceedings{pmlr-v70-sivakumar17a, 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.}, added-at = {2021-12-07T07:39:57.000+0100}, author = {Sivakumar, Vidyashankar and Banerjee, Arindam}, biburl = {https://www.bibsonomy.org/bibtex/2ccd65ab9569f9b055e7021f4365a8604/annakrause}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, description = {High-Dimensional Structured Quantile Regression}, editor = {Precup, Doina and Teh, Yee Whye}, interhash = {1d2f7d2e613da31ec265293cc663eb25}, intrahash = {ccd65ab9569f9b055e7021f4365a8604}, keywords = {todo:neurips}, month = {06--11 Aug}, pages = {3220--3229}, pdf = {http://proceedings.mlr.press/v70/sivakumar17a/sivakumar17a.pdf}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, timestamp = {2021-12-07T07:39:57.000+0100}, title = {High-Dimensional Structured Quantile Regression}, url = {https://proceedings.mlr.press/v70/sivakumar17a.html}, volume = 70, year = 2017 }