  Deep neural networks (DNNs) have successfully learned useful data
representations in various tasks. However, assessing the reliability of these
representations remains a challenge. Deep Ensemble is widely considered the
state-of-the-art method which can estimate the uncertainty with higher quality,
but it is very expensive to train and test. MC-Dropout is another popular
method, which is less expensive but lacks the diversity of predictions. To
estimate the uncertainty with higher quality in less time, we introduce a
ReLU-Based Uncertainty Estimation (RBUE) method. Instead of randomly dropping
some neurons of the network as in MC-Dropout or using the randomness of the
initial weights of networks as in Deep Ensemble, RBUE adds randomness to the
activation function module, making the outputs diverse. Under the method, we
propose two strategies, MC-DropReLU and MC-RReLU, to estimate uncertainty. We
analyze and compare the output diversity of MC-Dropout and our method from the
variance perspective and obtain the relationship between the hyperparameters
and predictive diversity in the two methods. Moreover, our method is simple to
implement and does not need to modify the existing model. We experimentally
validate the RBUE on three widely used datasets, CIFAR10, CIFAR100, and
TinyImageNet. The experiments demonstrate that our method has competitive
performance but is more favorable in training time and memory requirements.
