TY - GEN
T1 - High-dimensional structured quantile regression
AU - Sivakumar, Vidyashankar
AU - Banerjee, Arindam
N1 - Publisher Copyright:
Copyright © 2017 by the authors.
PY - 2017
Y1 - 2017
N2 - Quantile regression aims at modeling the conditional median and quantilcs 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.
AB - Quantile regression aims at modeling the conditional median and quantilcs 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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M3 - Conference contribution
AN - SCOPUS:85048469942
T3 - 34th International Conference on Machine Learning, ICML 2017
SP - 4953
EP - 4962
BT - 34th International Conference on Machine Learning, ICML 2017
PB - International Machine Learning Society (IMLS)
T2 - 34th International Conference on Machine Learning, ICML 2017
Y2 - 6 August 2017 through 11 August 2017
ER -