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

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.

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Cited by in corpus (9)

• Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations
• Advances in Variational Inference
• Fast Variational Inference for Bayesian Factor Analysis in Single and Multi-Study Settings
• Variational Bayesian Inference for Mixed Logit Models with Unobserved Inter- and Intra-Individual Heterogeneity
• Discrete Choice Analysis with Machine Learning Capabilities
• Variational inference for hierarchical models with conditional scale and skewness corrections
• Pólygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models
• Scalable Variational Inference for Multinomial Probit Models under Large Choice Sets and Sample Sizes
• Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services