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 noisecontrastive 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.
Original language | English |
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Title of host publication | Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS 2019) |
Place of Publication | Naha, Okinawa, Japan |
Publisher | PMLR |
Pages | 2741-2750 |
Number of pages | 14 |
Volume | 89 |
Publication status | Published - 25 Apr 2019 |
Event | 22nd International Conference on Artificial Intelligence and Statistics - Naha, Japan Duration: 16 Apr 2019 → 18 Apr 2019 https://www.aistats.org/ |
Publication series
Name | Proceedings of Machine Learning Research |
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Publisher | PMLR |
Volume | 89 |
ISSN (Electronic) | 2640-3498 |
Conference
Conference | 22nd International Conference on Artificial Intelligence and Statistics |
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Abbreviated title | AISTATS 2019 |
Country/Territory | Japan |
City | Naha |
Period | 16/04/19 → 18/04/19 |
Internet address |