  We propose a generic framework to calibrate accuracy and confidence of a
prediction in deep neural networks through stochastic inferences. We interpret
stochastic regularization using a Bayesian model, and analyze the relation
between predictive uncertainty of networks and variance of the prediction
scores obtained by stochastic inferences for a single example. Our empirical
study shows that the accuracy and the score of a prediction are highly
correlated with the variance of multiple stochastic inferences given by
stochastic depth or dropout. Motivated by this observation, we design a novel
variance-weighted confidence-integrated loss function that is composed of two
cross-entropy loss terms with respect to ground-truth and uniform distribution,
which are balanced by variance of stochastic prediction scores. The proposed
loss function enables us to learn deep neural networks that predict confidence
calibrated scores using a single inference. Our algorithm presents outstanding
confidence calibration performance and improves classification accuracy when
combined with two popular stochastic regularization techniques---stochastic
depth and dropout---in multiple models and datasets; it alleviates
overconfidence issue in deep neural networks significantly by training networks
to achieve prediction accuracy proportional to confidence of prediction.
