Neural Inference with Incomplete Data

Abstract

Leveraging their computational speed and flexibility, neural networks are increasingly being used to facilitate fast, simulation-based statistical inference. However, it is not straightforward to use neural networks with data that for various reasons are incomplete, which precludes their use in many applications. In this work, we investigate two approaches for addressing this challenge. First, a masking approach, where an appropriately padded data vector and a corresponding missingness-pattern indicator are input to a neural network. Second, an expectation-maximization (EM) approach, based on the Monte Carlo EM algorithm, in which the E- and M-steps are approximated using conditional simulation and a neural network that outputs a maximum a posteriori (MAP) estimate from the completed data. We compare the two approaches to missingness using simulated incomplete data from a variety of spatial models. The utility of the methodology is shown on Arctic sea-ice data, analysed using a novel hidden Potts model with an intractable likelihood.