Title: High-dimensional copula variational approximation through transformation
Authors: David Nott - National University of Singapore (Singapore) [presenting]
Michael Smith - University of Melbourne (Australia)
Ruben Loaiza-Maya - Monash University (Australia)
Abstract: Variational approximation methods are attractive for computing posterior inferences for highly parametrized models and large datasets. They approximate a target distribution - either the posterior or an augmented posterior - using a simpler distribution that is selected to balance accuracy with computational feasibility. We approximate an element-wise parametric transformation of the target distribution as multivariate Gaussian or skew-normal. Approximations of this kind are copula models for the original parameters, with an implicit Gaussian or skew-normal copula function and flexible parametric margins. A key observation is that their adoption can improve the accuracy of variational inference in high dimensions at limited computational cost. To illustrate, we consider the Yeo-Johnson and G\&H transformations of the target distribution, along with sparse factor structures for the scale matrix of the Gaussian or skew-normal. We also show how to implement efficient reparametrization gradient methods for these implicit copula models. The efficacy of the approach is illustrated in a number of examples. In each case, we show that the proposed copula model distributions can be more accurate variational approximations than the equivalent Gaussian distributions, but at only a minor increase in computational cost.