Maximum likelihood estimation for the $λ$-exponential family
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908352000294912 |
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| author | Tian, Xiwei Wong, Ting-Kam Leonard Yang, Jiaowen Zhang, Jun |
| author_facet | Tian, Xiwei Wong, Ting-Kam Leonard Yang, Jiaowen Zhang, Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood estimation for the $λ$-exponential family Tian, Xiwei Wong, Ting-Kam Leonard Yang, Jiaowen Zhang, Jun Statistics Theory 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. |
| title | Maximum likelihood estimation for the $λ$-exponential family |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2505.03582 |