Retrospective Uncertainties for Deep Models using Vine Copulas

Abstract

Despite the major progress of deep models as learning machines, uncertainty estimation remains a major challenge. Existing solutions rely on modified loss functions or architectural changes. We propose to compensate for the lack of built-in uncertainty estimates by supplementing any network, retrospectively, with a subsequent vine copula model, in an overall compound we call Vine-Copula Neural Network (VCNN). Through synthetic and real-data experiments, we show that VCNNs could be task (regression/classification) and architecture (recurrent, fully connected) agnostic while providing reliable and better-calibrated uncertainty estimates, comparable to state-of-the-art built-in uncertainty solutions.The research leading to these results has received funding from the Horizon Europe Programme under the SAFEXPLAIN Project (www.safexplain.eu), grant agreement num. 101069595 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 772773). Additionally, this work has been partially supported by Grant PID2019-107255GB-C21 funded by MCIN/AEI/ 10.13039/501100011033.Peer ReviewedPostprint (published version