  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.
