Deep Evidential Learning for Bayesian Quantile Regression
Frederik Boe Hüttel Filipe Rodrigues Francisco Câmara Pereira
It is desirable to have accurate uncertainty estimation from a single
deterministic forward-pass model, as traditional methods for uncertainty
quantification are computationally expensive. However, this is difficult
because single forward-pass models do not sample weights during inference and
often make assumptions about the target distribution, such as assuming it is
Gaussian. This can be restrictive in regression tasks, where the mean and
standard deviation are inadequate to model the target distribution accurately.
This paper proposes a deep Bayesian quantile regression model that can estimate
the quantiles of a continuous target distribution without the Gaussian
assumption. The proposed method is based on evidential learning, which allows
the model to capture aleatoric and epistemic uncertainty with a single
deterministic forward-pass model. This makes the method efficient and scalable
to large models and datasets. We demonstrate that the proposed method achieves
calibrated uncertainties on non-Gaussian distributions, disentanglement of
aleatoric and epistemic uncertainty, and robustness to out-of-distribution
samples.