Estimating Large-Scale Tree Logit Models

Srikanth Jagabathula (), Paat Rusmevichientong (), Ashwin Venkataraman () and Xinyi Zhao ()
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Srikanth Jagabathula: Stern School of Business, New York University, New York, New York 10012
Paat Rusmevichientong: Marshall School of Business, University of Southern California, Los Angeles, California 90089
Ashwin Venkataraman: Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080
Xinyi Zhao: Amazon Advertising, Palo Alto, California 94301

Operations Research, 2024, vol. 72, issue 1, 257-276

Abstract: 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 large-scale tree logit models with thousands of nodes.

Keywords: Market Analytics and Revenue Management; tree logit; choice modeling; parameter estimation; MM (majorize-minimize) algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:1:p:257-276

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