  From the statistical learning perspective, complexity control via explicit
regularization is a necessity for improving the generalization of
over-parameterized models. However, the impressive generalization performance
of neural networks with only implicit regularization may be at odds with this
conventional wisdom. In this work, we revisit the importance of explicit
regularization for obtaining well-calibrated predictive uncertainty.
Specifically, we introduce a probabilistic measure of calibration performance,
which is lower bounded by the log-likelihood. We then explore explicit
regularization techniques for improving the log-likelihood on unseen samples,
which provides well-calibrated predictive uncertainty. Our findings present a
new direction to improve the predictive probability quality of deterministic
neural networks, which can be an efficient and scalable alternative to Bayesian
neural networks and ensemble methods.
