Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning

TL;DR

This paper introduces a Bayesian Deep Learning model that effectively quantifies uncertainty in skewed, discrete-continuous data, improving predictions in climate super-resolution tasks and potentially benefiting other fields with extreme value considerations.

Contribution

It presents the first uncertainty quantification model in statistical downscaling that captures both aleatoric and epistemic uncertainties using discrete-continuous likelihoods, especially for skewed data.

Findings

Discrete-continuous models outperform Gaussian in accuracy and calibration.

Lognormal likelihood provides better uncertainty estimates at distribution extremes.

First model to characterize both aleatoric and epistemic uncertainties in statistical downscaling.

Abstract

Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component, well-characterized uncertainty estimates must accompany predictions. However, S&E observations and model-simulations often follow heavily skewed distributions and are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean, likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture uncertainties from noisy observations, aleatoric, and from unknown model parameters, epistemic, provide us a foundation. Here we present a discrete-continuous BDL model with Gaussian and lognormal likelihoods for uncertainty quantification (UQ). We demonstrate the approach by developing UQ estimates on `DeepSD', a super-resolution based DL model for Statistical Downscaling (SD) in climate applied to precipitation, which follows an extremely skewed distribution. We find that the discrete-continuous models outperform a basic Gaussian distribution in terms of predictive accuracy and uncertainty calibration. Furthermore, we find that the lognormal distribution, which can handle skewed distributions, produces quality uncertainty estimates at the extremes. Such results may be important across S&E, as well as other domains such as finance and economics, where extremes are often of significant interest. Furthermore, to our knowledge, this is the first UQ model in SD where both aleatoric and epistemic uncertainties are characterized.