Maximum likelihood estimation for the λ-exponential family

2025/05/06 by Tian, Xiwei, Wong, Ting-Kam Leonard, Yang, Jiaowen +1
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2505.03582

Abstract

The λ-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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