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While Bayesian neural networks have many appealing characteristics, currentpriors do not easily allow users to specify basic properties such as expectedlengthscale or amplitude variance. In this work, we introduce Poisson ProcessRadial Basis Function Networks, a novel prior that is able to encode amplitudestationarity and input-dependent lengthscale. We prove that our novelformulation allows for a decoupled specification of these properties, and thatthe estimated regression function is consistent as the number of observationstends to infinity. We demonstrate its behavior on synthetic and real examples.

Towards Expressive Priors for Bayesian Neural Networks: Poisson Process Radial Basis Function Networks