Exploiting compositionality to explore a large space of model structures

Roger Grosse, Ruslan R Salakhutdinov, William T. Freeman, Joshua B. Tenenbaum
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:304-313, 2012.

Abstract

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-grosse12a, title = {Exploiting compositionality to explore a large space of model structures}, author = {Grosse, Roger and Salakhutdinov, Ruslan R and Freeman, William T. and Tenenbaum, Joshua B.}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {304--313}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/grosse12a/grosse12a.pdf}, url = {https://proceedings.mlr.press/r10/grosse12a.html}, abstract = {The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Exploiting compositionality to explore a large space of model structures %A Roger Grosse %A Ruslan R Salakhutdinov %A William T. Freeman %A Joshua B. Tenenbaum %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-grosse12a %I PMLR %P 304--313 %U https://proceedings.mlr.press/r10/grosse12a.html %V R10 %X The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code. %Z Reissued by PMLR on 04 October 2026.
APA
Grosse, R., Salakhutdinov, R.R., Freeman, W.T. & Tenenbaum, J.B.. (2012). Exploiting compositionality to explore a large space of model structures. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:304-313 Available from https://proceedings.mlr.press/r10/grosse12a.html. Reissued by PMLR on 04 October 2026.

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