While deep neural networks (NNs) do not provide the confidence of its prediction, Bayesian neural network (BNN) can estimate the uncertainty of the prediction. However, BNNs have not been widely used in practice due to the computational cost of inference. This prohibitive computational cost is a hindrance especially when processing stream data with low-latency. To address this problem, we propose a novel model which approximate BNNs for data streams. Instead of generating separate prediction for each data sample independently, this model estimates the increments of prediction for a new data sample from the previous predictions. The computational cost of this model is almost the same as that of non-Bayesian NNs. Experiments with semantic segmentation on real-world data show that this model performs significantly faster than BNNs, estimating uncertainty comparable to the results of BNNs.
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