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Estimating Large-Scale Tree Logit Models

Author

Listed:
  • 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)

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.

Suggested Citation

  • Srikanth Jagabathula & Paat Rusmevichientong & Ashwin Venkataraman & Xinyi Zhao, 2024. "Estimating Large-Scale Tree Logit Models," Operations Research, INFORMS, vol. 72(1), pages 257-276, January.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:1:p:257-276
    DOI: 10.1287/opre.2023.2479
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