Neural Clustering Processes
This addresses the bottleneck of posterior inference in clustering models for researchers and practitioners in statistics and machine learning, offering a more efficient and scalable solution.
The paper tackles the problem of slow and inaccurate posterior inference in probabilistic clustering models by introducing deep network architectures that generate approximate posterior samples of cluster labels for datasets of any size, achieving this with either O(N) or O(K) network forward passes. As a result, they demonstrate a novel application to neural spike sorting for high-density multielectrode arrays.
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be inaccurate and/or very slow. In this work we introduce deep network architectures trained with labeled samples from any generative model of clustered datasets. At test time, the networks generate approximate posterior samples of cluster labels for any new dataset of arbitrary size. We develop two complementary approaches to this task, requiring either O(N) or O(K) network forward passes per dataset, where N is the dataset size and K the number of clusters. Unlike previous approaches, our methods sample the labels of all the data points from a well-defined posterior, and can learn nonparametric Bayesian posteriors since they do not limit the number of mixture components. As a scientific application, we present a novel approach to neural spike sorting for high-density multielectrode arrays.