Maximum likelihood estimation for the $λ$-exponential family
By: Xiwei Tian , Ting-Kam Leonard Wong , Jiaowen Yang and more
Potential Business Impact:
Helps computers learn from data more accurately.
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.
Similar Papers
On a new robust method of inference for general time series models
Methodology
Makes computer predictions more accurate with messy data.
Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds
Data Structures and Algorithms
Learns private data patterns without revealing secrets.
Closed-form solutions for parameter estimation in exponential families based on maximum a posteriori equations
Methodology
Finds patterns in numbers faster without complex math.