Scaling Bayesian inference of mixed multinomial logit models to very large datasets

TL;DR

This paper introduces an advanced variational inference method leveraging stochastic backpropagation, automatic differentiation, and GPU acceleration to efficiently scale Bayesian inference in mixed multinomial logit models for very large datasets, improving speed without losing accuracy.

Contribution

It proposes an Amortized Variational Inference framework with normalizing flows, enabling scalable Bayesian inference for large datasets in mixed multinomial logit models, surpassing existing methods.

Findings

Achieves multiple orders of magnitude speedup over traditional methods

Maintains estimation accuracy despite increased computational efficiency

Effectively scales Bayesian inference to very large datasets

Abstract

Variational inference methods have been shown to lead to significant improvements in the computational efficiency of approximate Bayesian inference in mixed multinomial logit models when compared to standard Markov-chain Monte Carlo (MCMC) methods without compromising accuracy. However, despite their demonstrated efficiency gains, existing methods still suffer from important limitations that prevent them to scale to very large datasets, while providing the flexibility to allow for rich prior distributions and to capture complex posterior distributions. In this paper, we propose an Amortized Variational Inference approach that leverages stochastic backpropagation, automatic differentiation and GPU-accelerated computation, for effectively scaling Bayesian inference in Mixed Multinomial Logit models to very large datasets. Moreover, we show how normalizing flows can be used to increase the flexibility of the variational posterior approximations. Through an extensive simulation study, we empirically show that the proposed approach is able to achieve computational speedups of multiple orders of magnitude over traditional MSLE and MCMC approaches for large datasets without compromising estimation accuracy.