Title: Neural Clustering Processes. Abstract: Mixture models, a basic building block in countless statistical models, involve latent random variables over discrete spaces, and existing posterior inference methods can be inaccurate and/or very slow.  In this work we introduce a novel deep learning architecture for efficient amortized Bayesian inference over mixture models. While previous approaches to amortized clustering assumed a fixed or maximum number of mixture components and only amortized over the continuous parameters of each mixture component, our method amortizes over the local discrete labels of all the data points, and performs inference over an unbounded number of mixture components. The latter property makes our method natural for the challenging case of nonparametric Bayesian models, where the number of mixture components grows with the dataset. Our approach exploits the exchangeability of the generative models and is based on mapping distributed, permutation-invariant representations of discrete  arrangements into varying-size multinomial conditional probabilities. The resulting algorithm parallelizes easily, yields iid samples from the approximate posteriors along with a normalized probability estimate of each sample (a quantity generally unavailable using Markov Chain Monte Carlo) and can easily be applied to both conjugate and non-conjugate models, as training only requires samples from the generative model. We also present an extension of the method to models of random communities (such as infinite relational or stochastic block models). As a scientific application, we present a novel approach to neural spike sorting for high-density multielectrode arrays. 
