A0252
Title: Fast and accurate variational inference for models with many latent variables
Authors: Ruben Loaiza-Maya - Monash University (Australia)
David Nott - National University of Singapore (Singapore)
Peter Danaher - Monash University (Austria)
Michael Smith - University of Melbourne (Australia) [presenting]
Abstract: Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular alternative. Key to the success of these is the selection of an approximation to the target density that is accurate, tractable and fast to calibrate using optimization methods. Most existing choices can be inaccurate or slow to calibrate when there are many latent variables. We propose a family of tractable variational approximations that are more accurate and faster to calibrate for this case. We derive a simplified expression for the re-parameterization gradient of the variational lower bound, which is the main ingredient of efficient optimization algorithms used to implement variational estimation. We illustrate using a random coefficients Tobit model applied to two million sales by 20,000 individuals in a large consumer panel from a marketing study. Last, we show how to implement data sub-sampling in variational inference for our approximation, which can lead to a further reduction in computation time.
