Variational Inference on the Final-Layer Output of Neural Networks

Traditional neural networks are simple to train but they typically produce overconfident predictions. In contrast, Bayesian neural networks provide good uncertainty quantification but optimizing them is time consuming due to the large parameter space. This paper proposes to combine the advantages of both approaches by performing Variational Inference in the Final layer Output space (VIFO), because the output space is much smaller than the parameter space. We use neural networks to learn the mean and the variance of the probabilistic output. Like standard, non-Beyesian models, VIFO enjoys simple training and one can use Rademacher complexity to provide risk bounds for the model. On the other hand, using the Bayesian formulation we incorporate collapsed variational inference with VIFO which significantly improves the performance in practice. Experiments show that VIFO and ensembles of VIFO provide a good tradeoff in terms of run time and uncertainty quantification, especially for out of distribution data.