Forward Amortized Inference for LikelihoodFree Variational Marginalization
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Proceedings of Machine Learning Research, PMLR 89:777786, 2019.
Abstract
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a jointcontrastive variational loss. The resulting forward amortized variational inference is a likelihoodfree method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized meanfield approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful metaclassification network that can solve arbitrary classification problems without further training.
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