Variational Noise-Contrastive Estimation
This provides a new technique for researchers and practitioners working with unnormalised models, addressing a bottleneck in statistical learning, though it builds incrementally on existing methods like NCE and VI.
The paper tackles the intractable parameter learning problem for unnormalised latent variable models by proposing variational noise-contrastive estimation (VNCE), which extends NCE using a variational lower bound, enabling both parameter estimation and posterior inference with demonstrated applicability to toy models and a realistic graphical model estimation task.
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.