TY - GEN

T1 - Bi-level path following for cross validated solution of kernel quantile regression

AU - Rosset, Saharon

PY - 2008

Y1 - 2008

N2 - Modeling of conditional quantiles requires specification of the quantile being estimated and can thus be viewed as a parameterized predictive modeling problem. Quantile loss is typically used, and it is indeed parameterized by a quantile parameter. In this paper we show how to follow the path of cross validated solutions to regularized kernel quantile regression. Even though the bi-level optimization problem we encounter for every quantile is non-convex, the manner in which the optimal cross-validated solution evolves with the parameter of the loss function allows tracking of this solution. We prove this property, construct the resulting algorithm, and demonstrate it on data. This algorithm allows us to efficiently solve the whole family of bi-level problems.

AB - Modeling of conditional quantiles requires specification of the quantile being estimated and can thus be viewed as a parameterized predictive modeling problem. Quantile loss is typically used, and it is indeed parameterized by a quantile parameter. In this paper we show how to follow the path of cross validated solutions to regularized kernel quantile regression. Even though the bi-level optimization problem we encounter for every quantile is non-convex, the manner in which the optimal cross-validated solution evolves with the parameter of the loss function allows tracking of this solution. We prove this property, construct the resulting algorithm, and demonstrate it on data. This algorithm allows us to efficiently solve the whole family of bi-level problems.

UR - http://www.scopus.com/inward/record.url?scp=56449126749&partnerID=8YFLogxK

U2 - 10.1145/1390156.1390262

DO - 10.1145/1390156.1390262

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AN - SCOPUS:56449126749

SN - 9781605582054

T3 - Proceedings of the 25th International Conference on Machine Learning

SP - 840

EP - 847

BT - Proceedings of the 25th International Conference on Machine Learning

PB - Association for Computing Machinery (ACM)

T2 - 25th International Conference on Machine Learning

Y2 - 5 July 2008 through 9 July 2008

ER -