A0864
Title: Fast variational inference for multinomial probit models
Authors: Ruben Loaiza-Maya - Monash University (Australia) [presenting]
Didier Nibbering - Monash University (Australia)
Abstract: The multinomial probit model is often used to analyze choice behaviour. However, estimation with existing Markov Chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice data sets. A variational inference method is proposed that is fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of the variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large number of choice alternatives and a large number of observations. The accuracy and scalability of our method are illustrated in numerical experiments and real purchase data with one million observations
