  Deep neural networks have outperformed existing machine learning models in
various molecular applications. In practical applications, it is still
difficult to make confident decisions because of the uncertainty in predictions
arisen from insufficient quality and quantity of training data. Here, we show
that Bayesian neural networks are useful to quantify the uncertainty of
molecular property prediction with three numerical experiments. In particular,
it enables us to decompose the predictive variance into the model- and
data-driven uncertainties, which helps to elucidate the source of errors. In
the logP predictions, we show that data noise affected the data-driven
uncertainties more significantly than the model-driven ones. Based on this
analysis, we were able to find unexpected errors in the Harvard Clean Energy
Project dataset. Lastly, we show that the confidence of prediction is closely
related to the predictive uncertainty by performing on bio-activity and
toxicity classification problems.
