Fig. 2
From: Explainable uncertainty quantifications for deep learning-based molecular property prediction
Distribution mean and variance predicted by (A) a neural network model and (B) Deep Ensembles. Because Deep Ensembles estimate the mean value \({\mu }_{ens}\) by averaging the predicted means of \(M\) neural networks, the variance associated with Deep Ensembles (\({\sigma }_{ale}^{2}\)) is expected to be lower than the variance of one network in the ensemble (\({\sigma }_{m}^{2}\)). Therefore, one may overestimate \({\sigma }_{ale}^{2}\) by averaging \({\sigma }_{m}^{2}\) of networks in the ensemble (Eq. 5). This problem can be resolved by refining the weights in the variance layers (highlighted in yellow) to minimize the heteroscedastic loss function calculated with \({\mu }_{ens}\) and \({\sigma }_{ale}^{2}\) in the second round of training. FC, ML, and VL layers refer to the fully-connected layer, mean layer, and variance layer