ANC Workshop: Ben Rhodes and Steven Kleinegesse, Chair: Lazar Valkov

Ben Rhodes

 

Title: Variational noise-contrastive estimation

 

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

 

Joint work with Michael Gutmann

 

 

Steven Kleinegesse

 

Title: Efficient Bayesian Experimental Design for Implicit Models

 

Abstract: Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search. We find that this increases efficiency and allows us to consider higher design dimensions.