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arXiv · 2505.03582

Maximum likelihood estimation for the $\lambda$-exponential family

Xiwei Tian·Ting-Kam Leonard Wong·Jiaowen Yang·Jun Zhang
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Abstract

The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric point of view, but the development of computational methodologies is still in an early stage. In this paper, we propose a fixed point iteration for maximum likelihood estimation under i.i.d.~sampling, and prove using the duality that the likelihood is monotone along the iterations. We illustrate the algorithm with the $q$-Gaussian distribution and the Dirichlet perturbation.

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Xiwei Tian, Ting-Kam Leonard Wong, Jiaowen Yang, Jun Zhang. 2025-05-06. Maximum likelihood estimation for the $\lambda$-exponential family. https://arxiv.org/abs/2505.03582

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