  This paper proposes a dual-supervised uncertainty inference (DS-UI) framework
for improving Bayesian estimation-based uncertainty inference (UI) in deep
neural network (DNN)-based image recognition. In the DS-UI, we combine the
classifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixture
of Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existing
UI methods for DNNs, which only calculate the means or modes of the DNN
outputs' distributions, the proposed MoGMM-FC layer acts as a probabilistic
interpreter for the features that are inputs of the classifier to directly
calculate the probability density of them for the DS-UI. In addition, we
propose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB)
algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB and
optimization algorithms in other UI methods, the DS-SGVB not only models the
samples in the specific class for each Gaussian mixture model (GMM) in the
MoGMM, but also considers the negative samples from other classes for the GMM
to reduce the intra-class distances and enlarge the inter-class margins
simultaneously for enhancing the learning ability of the MoGMM-FC layer in the
DS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UI
methods in misclassification detection. We further evaluate the DS-UI in
open-set out-of-domain/-distribution detection and find statistically
significant improvements. Visualizations of the feature spaces demonstrate the
superiority of the DS-UI.
