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.
@article{arxiv.2107.06393,
title = {Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interface},
author = {Tuan Anh Le and Katherine M. Collins and Luke Hewitt and Kevin Ellis and N. Siddharth and Samuel J. Gershman and Joshua B. Tenenbaum},
journal= {arXiv preprint arXiv:2107.06393},
year = {2022}
}