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Title: Learning multiple quantiles with neural networks Authors:  SangJun Moon - University of Seoul (Korea, South) [presenting]
Jong-june Jeon - University of Seoul (Korea, South)
Jason Sang Hun Lee - University of Seoul (Korea, South)
Yongdai Kim - Seoul National University (Korea, South)
Abstract: A neural network model is presented to estimate multiple conditional quantiles satisfying the non-crossing property. Motivated by linear non-crossing quantile regression, we apply inequality constraints used in the developed model to learning the neural network with a feasible set. In particular, to use the first-order optimization method on the feasible set, we develop a modified version of the interior point method. In the algorithm, an auxiliary variable lying on the feasible set is introduced as a proxy of the model parameter in the barrier function. By regularizing the difference between the auxiliary and original parameters, our proposed algorithm achieves close to the optimal solution while avoiding the projected gradient step with polynomial computation to significantly improve the computational efficiency. We compare predictive performances of multiple quantiles regression with neural networks with those of existing neural network models and apply our proposed model to the prediction of real data.