ANC Workshop - 06/05/2025

Speaker: Kian Ming A. Chai (DSO National Laboratories, Singapore) 

Title: Variational Learning of Fractional Posteriors

Abstract:  We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors, offering a versatile tool for probabilistic modelling. We demonstrate two cases where gradients can be obtained analytically and a simulation study on mixture models showing that our fractional posteriors can be used to achieve better calibration compared to posteriors from the conventional variational bound. When applied to variational autoencoders (VAEs), our approach attains higher evidence bounds and enables learning of high-performing approximate Bayes posteriors jointly with fractional posteriors. We show that VAEs trained with fractional posteriors produce decoders that are better aligned for generation from the prior.  Joint work with Edwin V. Bonilla

Speaker: Chris Williams

Title: Fusing Foveal Fixations Using Linear Retinal Transformations and Bayesian Experimental Design

Abstract:  Humans (and most vertebrates) face the problem of fusing together multiple fixations of a scene in order to obtain a representation of the whole, where each fixation uses a high-resolution fovea and decreasing resolution in the periphery.  In this paper we explicitly represent the retinal transformation of a fixation as a linear downsampling of a high-resolution latent image of the scene, exploiting the known geometry.  This linear transformation allows us to carry out exact inference for the latent variables in factor analysis (FA) and mixtures of FA models of the scene. Further, this allows us to formulate and solve the choice of "where to look next" as a Bayesian experimental design problem. Experiments on the Frey faces and MNIST datasets demonstrate the effectiveness of our models.