  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.
