Variational inference for high-dimensional integrated choice and latent variable (ICLV) models within a Bayesian framework

Abstract

The variational Bayes is widely used to deal with high-dimensional models. The present study attempts to apply variational inference (VI) to estimate high-dimensional integrated choice and latent variable (ICLV) models. When utilizing the Maximum Simulated Likelihood (MSL) technique to calibrate an ICLV model with the Gaussian kernel, the log-likelihood function cannot be evaluated if the dimension of latent variables and choice options grows. Addressing this, the present study proposes a conditional variational inference (CVI) method that consistently estimate an ICLV model regardless of the dimensions of choice options and latent variables within a Bayesian framework. Variational models are supplanted by neural embedding, and the mean and variance of the Gaussian probability density are parameterized by a neural network, which is called the reparameterization trick. Furthermore, the Gumbel softmax function approximates the ’argmax’ operation for selecting a choice option of the maximum utility, which bypasses the computationally intensive task of calculating choice probabilities. Collectively, these strategies ensure the scalable ICLV model estimation, as increasing the number of latent variables and choice options. The calibration method succeeded in reproducing parameters of a large-scale ICLV model with 30 latent variables and 30 choice options.