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Traditional neural networks are simple to train but they typically produceoverconfident predictions. In contrast, Bayesian neural networks provide gooduncertainty quantification but optimizing them is time consuming due to thelarge parameter space. This paper proposes to combine the advantages of bothapproaches by performing Variational Inference in the Final layer Output space(VIFO), because the output space is much smaller than the parameter space. Weuse neural networks to learn the mean and the variance of the probabilisticoutput. Like standard, non-Beyesian models, VIFO enjoys simple training and onecan use Rademacher complexity to provide risk bounds for the model. On theother hand, using the Bayesian formulation we incorporate collapsed variationalinference with VIFO which significantly improves the performance in practice.Experiments show that VIFO and ensembles of VIFO provide a good tradeoff interms of run time and uncertainty quantification, especially for out ofdistribution data.

Variational Inference on the Final-Layer Output of Neural Networks