Leveraging the Exact Likelihood of Deep Latent Variable Models
This work addresses inferential issues in deep latent variable models for researchers and practitioners, offering incremental improvements in estimation and imputation.
The paper tackled the problem of unbounded likelihood in deep latent variable models, showing it causes mode collapse, and proposed methods to ensure maximum likelihood estimates and a missing data imputation algorithm that significantly outperforms existing schemes on several datasets.
Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. The purpose of this work is to study the general properties of this quantity and to show how they can be leveraged in practice. We focus on important inferential problems that rely on the likelihood: estimation and missing data imputation. First, we investigate maximum likelihood estimation for DLVMs: in particular, we show that most unconstrained models used for continuous data have an unbounded likelihood function. This problematic behaviour is demonstrated to be a source of mode collapse. We also show how to ensure the existence of maximum likelihood estimates, and draw useful connections with nonparametric mixture models. Finally, we describe an algorithm for missing data imputation using the exact conditional likelihood of a deep latent variable model. On several data sets, our algorithm consistently and significantly outperforms the usual imputation scheme used for DLVMs.