Censored Quantile Regression Neural Networks

• URL: http://arxiv.org/abs/2205.13496v1
• Date: Thu, 26 May 2022 17:10:28 GMT
• Title: Censored Quantile Regression Neural Networks
• Authors: Tim Pearce, Jong-Hyeon Jeong, Yichen Jia, Jun Zhu
• Abstract summary: This paper considers doing quantile regression on censored data using neural networks (NNs) We show how an algorithm popular in linear models can be applied to NNs. Our major contribution is a novel algorithm that simultaneously optimises a grid of quantiles output by a single NN.
• Score: 24.118509578363593
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of uncertainty, using a flexible function approximator. We begin by showing how an algorithm popular in linear models can be applied to NNs. However, the resulting procedure is inefficient, requiring sequential optimisation of an individual NN at each desired quantile. Our major contribution is a novel algorithm that simultaneously optimises a grid of quantiles output by a single NN. To offer theoretical insight into our algorithm, we show firstly that it can be interpreted as a form of expectation-maximisation, and secondly that it exhibits a desirable `self-correcting' property. Experimentally, the algorithm produces quantiles that are better calibrated than existing methods on 10 out of 12 real datasets.

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