  Deep neural networks (DNNs) have achieved state-of-the-art performances in
many important domains, including medical diagnosis, security, and autonomous
driving. In these domains where safety is highly critical, an erroneous
decision can result in serious consequences. While a perfect prediction
accuracy is not always achievable, recent work on Bayesian deep networks shows
that it is possible to know when DNNs are more likely to make mistakes. Knowing
what DNNs do not know is desirable to increase the safety of deep learning
technology in sensitive applications. Bayesian neural networks attempt to
address this challenge. However, traditional approaches are computationally
intractable and do not scale well to large, complex neural network
architectures. In this paper, we develop a theoretical framework to approximate
Bayesian inference for DNNs by imposing a Bernoulli distribution on the model
weights. This method, called MC-DropConnect, gives us a tool to represent the
model uncertainty with little change in the overall model structure or
computational cost. We extensively validate the proposed algorithm on multiple
network architectures and datasets for classification and semantic segmentation
tasks. We also propose new metrics to quantify the uncertainty estimates. This
enables an objective comparison between MC-DropConnect and prior approaches.
Our empirical results demonstrate that the proposed framework yields
significant improvement in both prediction accuracy and uncertainty estimation
quality compared to the state of the art.
