Title: Variational Implicit Processes,
Abstract: This paper introduces the variational implicit processes (VIPs), a Bayesian
nonparametric method based on a class of highly flexible priors over functions.
Similar to Gaussian processes (GPs), in implicit processes (IPs), an implicit
multivariate prior (data simulators, Bayesian neural networks, etc.) is placed
over any finite collections of random variables. A novel and efficient
variational inference algorithm for IPs is derived using wake-sleep updates,
which gives analytic solutions and allows scalable hyper-parameter learning
with stochastic optimization. Experiments on real-world regression datasets
demonstrate that VIPs return better uncertainty estimates and superior
performance over existing inference methods for GPs and Bayesian neural
networks. With a Bayesian LSTM as the implicit prior, the proposed approach
achieves state-of-the-art results on predicting power conversion efficiency of
molecules based on raw chemical formulas.