Lifted Inference for Relational Continuous Models

Jaesik Choi, David Hill, Eyal Amir
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:134-142, 2010.

Abstract

Relational Continuous Models (RCMs) represent joint probability densities over attributes of ob- jects, when the attributes have continuous do- mains. With relational representations, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents a new exact lifted inference algorithm for RCMs, thus it scales up to large models of real world applications. The algorithm applies to Relational Pairwise Models which are (relational) products of potentials of arity 2. Our algorithm is unique in two ways. First, it substan- tially improves the efficiency of lifted inference with variables of continuous domains. When a relational model has Gaussian potentials, it takes only linear-time compared to cubic time of pre- vious methods. Second, it is the first exact infer- ence algorithm which handles RCMs in a lifted way. The algorithm is illustrated over an example from econometrics. Experimental results show that our algorithm outperforms both a ground- level inference algorithm and an algorithm built with previously-known lifted methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-choi10a, title = {Lifted Inference for Relational Continuous Models}, author = {Choi, Jaesik and Hill, David and Amir, Eyal}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {134--142}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/choi10a/choi10a.pdf}, url = {https://proceedings.mlr.press/r8/choi10a.html}, abstract = {Relational Continuous Models (RCMs) represent joint probability densities over attributes of ob- jects, when the attributes have continuous do- mains. With relational representations, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents a new exact lifted inference algorithm for RCMs, thus it scales up to large models of real world applications. The algorithm applies to Relational Pairwise Models which are (relational) products of potentials of arity 2. Our algorithm is unique in two ways. First, it substan- tially improves the efficiency of lifted inference with variables of continuous domains. When a relational model has Gaussian potentials, it takes only linear-time compared to cubic time of pre- vious methods. Second, it is the first exact infer- ence algorithm which handles RCMs in a lifted way. The algorithm is illustrated over an example from econometrics. Experimental results show that our algorithm outperforms both a ground- level inference algorithm and an algorithm built with previously-known lifted methods.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Lifted Inference for Relational Continuous Models %A Jaesik Choi %A David Hill %A Eyal Amir %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-choi10a %I PMLR %P 134--142 %U https://proceedings.mlr.press/r8/choi10a.html %V R8 %X Relational Continuous Models (RCMs) represent joint probability densities over attributes of ob- jects, when the attributes have continuous do- mains. With relational representations, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents a new exact lifted inference algorithm for RCMs, thus it scales up to large models of real world applications. The algorithm applies to Relational Pairwise Models which are (relational) products of potentials of arity 2. Our algorithm is unique in two ways. First, it substan- tially improves the efficiency of lifted inference with variables of continuous domains. When a relational model has Gaussian potentials, it takes only linear-time compared to cubic time of pre- vious methods. Second, it is the first exact infer- ence algorithm which handles RCMs in a lifted way. The algorithm is illustrated over an example from econometrics. Experimental results show that our algorithm outperforms both a ground- level inference algorithm and an algorithm built with previously-known lifted methods. %Z Reissued by PMLR on 04 October 2026.
APA
Choi, J., Hill, D. & Amir, E.. (2010). Lifted Inference for Relational Continuous Models. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:134-142 Available from https://proceedings.mlr.press/r8/choi10a.html. Reissued by PMLR on 04 October 2026.

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