Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interface

Tuan Anh Le, Katherine M. Collins, Luke Hewitt, Kevin Ellis, Siddharth N, Samuel Gershman, Joshua B. Tenenbaum

Keywords: wake-sleep, variational inference, neuro-symbolic generative models

Abstract: Modeling complex phenomena typically involves the use of both discrete and continuous variables. Such a setting applies across a wide range of problems, from identifying trends in time-series data to performing effective compositional scene understanding in images. Here, we propose Hybrid Memoised Wake-Sleep (HMWS), an algorithm for effective inference in such hybrid discrete-continuous models. Prior approaches to learning suffer as they need to perform repeated expensive inner-loop discrete inference. We build on a recent approach, Memoised Wake-Sleep (MWS), which alleviates part of the problem by memoising discrete variables, and extend it to allow for a principled and effective way to handle continuous variables by learning a separate recognition model used for importance-sampling based approximate inference and marginalization. We evaluate HMWS in the GP-kernel learning and 3D scene understanding domains, and show that it outperforms current state-of-the-art inference methods.