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Activity Number: 367 - Highlights of JCGS Publications 2021
Type: Invited
Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
Sponsor: Journal of Computational and Graphical Statistics
Abstract #319219
Title: Marginally Calibrated Deep Distributional Regression
Author(s): Michael Stanley Smith* and David Nott and Nadja Stanley Klein
Companies: University of Melbourne and University of Singapore and Humboldt University, Berlin
Keywords: Calibration; Copula; Deep Neural Network; Distributional Regression; Likelihood-free Inference
Abstract:

Until recently there has been little work on accurate uncertainty quantification for predictions from DNN regression models. We add to this literature by outlining an approach to constructing predictive distributions that are `marginally calibrated'. This is where the long run average of the predictive distributions of the response variable matches the observed empirical margin. Our approach considers a DNN regression with a conditionally Gaussian prior for the final layer weights, from which an implicit copula process on the feature space is extracted. This copula process is combined with a non-parametrically estimated marginal distribution for the response. The end result is a scalable distributional DNN regression method with marginally calibrated predictions. The approach is first illustrated using dense layer feed-forward neural networks. However, our main motivating application is in likelihood-free inference, where distributional deep regression is used to estimate marginal posterior distributions. We show that marginal calibration results in improved uncertainty quantification. Our approach also avoids the need for manual specification of summary statistics.


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