  Active learning methods for neural networks are usually based on greedy
criteria which ultimately give a single new design point for the evaluation.
Such an approach requires either some heuristics to sample a batch of design
points at one active learning iteration, or retraining the neural network after
adding each data point, which is computationally inefficient. Moreover,
uncertainty estimates for neural networks sometimes are overconfident for the
points lying far from the training sample. In this work we propose to
approximate Bayesian neural networks (BNN) by Gaussian processes, which allows
us to update the uncertainty estimates of predictions efficiently without
retraining the neural network, while avoiding overconfident uncertainty
prediction for out-of-sample points. In a series of experiments on real-world
data including large-scale problems of chemical and physical modeling, we show
superiority of the proposed approach over the state-of-the-art methods.
