not-MIWAE: Deep Generative Modelling with Missing not at Random Data

TL;DR

This paper introduces a deep generative modeling approach for data with missing not at random (MNAR), explicitly modeling the missingness process using neural networks to improve inference accuracy.

Contribution

It proposes a novel deep latent variable model that incorporates a neural network to model MNAR missingness, along with an importance-weighted variational inference method.

Findings

Explicitly modeling missingness improves inference accuracy.

The approach performs well on various datasets with different missingness patterns.

Neural network flexibility allows modeling complex missing data mechanisms.

Abstract

When a missing process depends on the missing values themselves, it needs to be explicitly modelled and taken into account while doing likelihood-based inference. We present an approach for building and fitting deep latent variable models (DLVMs) in cases where the missing process is dependent on the missing data. Specifically, a deep neural network enables us to flexibly model the conditional distribution of the missingness pattern given the data. This allows for incorporating prior information about the type of missingness (e.g. self-censoring) into the model. Our inference technique, based on importance-weighted variational inference, involves maximising a lower bound of the joint likelihood. Stochastic gradients of the bound are obtained by using the reparameterisation trick both in latent space and data space. We show on various kinds of data sets and missingness patterns that explicitly modelling the missing process can be invaluable.