Flexible, Nonlinear Probabilistic Downscaling Models: Conditional Density Estimation Networks and Quantile Regression Neural Networks

• Activity Number: 164
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Alex Cannon*+
• Companies: Pacific Climate Impacts Consortium
• Keywords: neural network ; stochastic weather generator ; quantile regression ; downscaling ; nonlinear

Abstract

Two probabilistic, nonlinear statistical downscaling models and their relationships with established downscaling models are described. A conditional density estimation network (CDEN) is a probabilistic extension of the multi-layer perceptron neural network (MLP). A CDEN model allows users to estimate parameters of a distribution conditioned upon predictors using the MLP architecture. The result is a flexible model for exceedance probabilities, prediction intervals, etc. from the specified conditional distribution. Nonlinear relationships, including those involving predictor interactions, can be described. Mixed discrete-continuous variables, like precipitation, can be specified using zero-inflated distributions. Multivariate distributions can be modelled via a mixture of multivariate Gaussians. A quantile regression neural network (QRNN) is an MLP analogue of quantile regression. The QRNN follows from previous work on the estimation of censored regression quantiles, thus allowing nonparametric predictions for mixed discrete-continuous variables. A differentiable version of the quantile regression cost function is adopted to allow the use of standard MLP optimization algorithms.