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Kernel Conditional Quantile Estimation via Reduction Revisited

Novi Quadrianto; Kristian Kersting; Mark D. Reid; Tibério S. Caetano; Wray L. Buntine
In: Wei Wang; Hillol Kargupta; Sanjay Ranka; Philip S. Yu; Xindong Wu (Hrsg.). ICDM 2009, The Ninth IEEE International Conference on Data Mining. IEEE International Conference on Data Mining (ICDM-2009), December 6-9, Miami, Florida, USA, Pages 938-943, IEEE Computer Society, 2009.


Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.

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