Stochastic variational inference for large-scale discrete choice models using adaptive batch sizes

TL;DR

This paper introduces stochastic variational inference methods with adaptive batch sizes for efficiently estimating large-scale mixed multinomial logit models, enabling scalable Bayesian discrete choice analysis.

Contribution

It develops and compares three variational inference approaches for MMNL models, incorporating adaptive minibatch strategies to improve scalability and convergence.

Findings

Stochastic variational inference achieves comparable accuracy to MCMC.

Adaptive batch size strategy accelerates convergence on large datasets.

Methods effectively handle correlated random coefficients in MMNL models.

Abstract

Discrete choice models describe the choices made by decision makers among alternatives and play an important role in transportation planning, marketing research and other applications. The mixed multinomial logit (MMNL) model is a popular discrete choice model that captures heterogeneity in the preferences of decision makers through random coefficients. While Markov chain Monte Carlo methods provide the Bayesian analogue to classical procedures for estimating MMNL models, computations can be prohibitively expensive for large datasets. Approximate inference can be obtained using variational methods at a lower computational cost with competitive accuracy. In this paper, we develop variational methods for estimating MMNL models that allow random coefficients to be correlated in the posterior and can be extended easily to large-scale datasets. We explore three alternatives: (1) Laplace variational inference, (2) nonconjugate variational message passing and (3) stochastic linear regression. Their performances are compared using real and simulated data. To accelerate convergence for large datasets, we develop stochastic variational inference for MMNL models using each of the above alternatives. Stochastic variational inference allows data to be processed in minibatches by optimizing global variational parameters using stochastic gradient approximation. A novel strategy for increasing minibatch sizes adaptively within stochastic variational inference is proposed.