Lifted Hybrid Variational Inference
This work addresses inference in hybrid probabilistic relational models, which is an incremental improvement over existing methods limited to discrete or restricted continuous domains.
The authors tackled the problem of performing inference in probabilistic relational models with hybrid domains, developing two approximate lifted variational methods that can handle multi-modality and continuous evidence. They demonstrated that their approach is scalable, exploits model symmetries, and compares favorably against existing message-passing methods in various settings.
A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions, e.g., Gaussian. We investigate two approximate lifted variational approaches that are applicable to hybrid domains and expressive enough to capture multi-modality. We demonstrate that the proposed variational methods are both scalable and can take advantage of approximate model symmetries, even in the presence of a large amount of continuous evidence. We demonstrate that our approach compares favorably against existing message-passing based approaches in a variety of settings. Finally, we present a sufficient condition for the Bethe approximation to yield a non-trivial estimate over the marginal polytope.