Estimating Large-Scale Tree Logit Models

• 成果类型: Article
• 署名作者: Jagabathula, Srikanth; Rusmevichientong, Paat; Venkataraman, Ashwin; Zhao, Xinyi
• 署名单位: New York University; University of Southern California; University of Texas System; University of Texas Dallas
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.2479
• 发表日期: 2024
• 关键词: tree logit; choice modeling; Parameter Estimation; MM (majorize-minimize) algorithm

摘要

We describe an efficient estimation method for large-scale tree logit models, using a novel change-of-variables transformation that allows us to express the negative log-likelihood as a strictly convex function in the leaf node parameters and a difference of strictly convex functions in the nonleaf node parameters. Exploiting this representation, we design a fast iterative method that computes a sequence of parameter estimates using simple closed-form updates. Our algorithm relies only on first-order information (function and gradients values), but unlike other first-order methods, it does not require any step size tuning or costly projection steps. The sequence of parameter estimates yields increasing likelihood values, and we establish sublinear convergence to a stationary point of the maximum likelihood problem. Numerical results on both synthetic and real data show that our algorithm outperforms state-of-the-art optimization methods, especially for largescale tree logit models with thousands of nodes.