Variational Noise-Contrastive Estimation

Benjamin Rhodes, Michael U. Gutmann
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2741-2750, 2019.

Abstract

Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the number of techniques in our arsenal, we propose variational noise-contrastive estimation (VNCE), building on NCE which is a method that only applies to unnormalised models. The core idea is to use a variational lower bound to the NCE objective function, which can be optimised in the same fashion as the evidence lower bound (ELBO) in standard variational inference (VI). We prove that VNCE can be used for both parameter estimation of unnormalised models and posterior inference of latent variables. The developed theory shows that VNCE has the same level of generality as standard VI, meaning that advances made there can be directly imported to the unnormalised setting. We validate VNCE on toy models and apply it to a realistic problem of estimating an undirected graphical model from incomplete data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-rhodes19a, title = {Variational Noise-Contrastive Estimation}, author = {Rhodes, Benjamin and Gutmann, Michael U.}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2741--2750}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/rhodes19a/rhodes19a.pdf}, url = {https://proceedings.mlr.press/v89/rhodes19a.html}, abstract = {Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the number of techniques in our arsenal, we propose variational noise-contrastive estimation (VNCE), building on NCE which is a method that only applies to unnormalised models. The core idea is to use a variational lower bound to the NCE objective function, which can be optimised in the same fashion as the evidence lower bound (ELBO) in standard variational inference (VI). We prove that VNCE can be used for both parameter estimation of unnormalised models and posterior inference of latent variables. The developed theory shows that VNCE has the same level of generality as standard VI, meaning that advances made there can be directly imported to the unnormalised setting. We validate VNCE on toy models and apply it to a realistic problem of estimating an undirected graphical model from incomplete data.} }
Endnote
%0 Conference Paper %T Variational Noise-Contrastive Estimation %A Benjamin Rhodes %A Michael U. Gutmann %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-rhodes19a %I PMLR %P 2741--2750 %U https://proceedings.mlr.press/v89/rhodes19a.html %V 89 %X Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the number of techniques in our arsenal, we propose variational noise-contrastive estimation (VNCE), building on NCE which is a method that only applies to unnormalised models. The core idea is to use a variational lower bound to the NCE objective function, which can be optimised in the same fashion as the evidence lower bound (ELBO) in standard variational inference (VI). We prove that VNCE can be used for both parameter estimation of unnormalised models and posterior inference of latent variables. The developed theory shows that VNCE has the same level of generality as standard VI, meaning that advances made there can be directly imported to the unnormalised setting. We validate VNCE on toy models and apply it to a realistic problem of estimating an undirected graphical model from incomplete data.
APA
Rhodes, B. & Gutmann, M.U.. (2019). Variational Noise-Contrastive Estimation. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2741-2750 Available from https://proceedings.mlr.press/v89/rhodes19a.html.

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