Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (2): 371-381.doi: 10.1007/s40305-021-00365-6

• Special Issue: Machine Learning and Optimization Algorithm • Previous Articles     Next Articles

A Gradient Descent Method for Estimating the Markov Chain Choice Model

Lei Fu, Dong-Dong Ge   

  1. School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China
  • Received:2021-06-24 Revised:2021-07-25 Online:2023-06-30 Published:2023-05-24
  • Contact: Dong-Dong Ge, Lei Fu E-mail:ge.dongdong@mail.shufe.edu.cn;leileifu@163.shufe.edu.cn

Abstract: In this paper, we propose a gradient descent method to estimate the parameters in a Markov chain choice model. Particularly, we derive closed-form formula for the gradient of the log-likelihood function and show the convergence of the algorithm. Numerical experiments verify the efficiency of our approach by comparing with the expectation-maximization algorithm. We show that the similar result can be extended to a more general case that one does not have observation of the no-purchase data.

Key words: Markov chain choice model, Parameter estimation, Gradient descent method

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