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Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the Hellinger divergence.
A relationship between the second derivatives of a convex function and of its conjugate
Jean-Pierre Crouzeix · 1977
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Estimation and moment recursion relations for multimodal distributions of the exponential family
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Markov random field image models and their applications to computer vision
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Statistical manifolds
Steffen L. Lauritzen · 1987
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Geometrical Foundations of Asymptotic Inference
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The Ising model is NP-complete
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Monte Carlo methods
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Kullback information of normal mixture is not an analytic function
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Mixed Bregman clustering with approximation guarantees
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Simplifying Gaussian mixture models via entropic quantization
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Distributed estimation, information loss and exponential families
Qiang Liu and Alexander T Ihler · 2014
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Reference duality and representation duality in information geometry
Jun Zhang · 2015
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Introduction to HPC with MPI for Data Science
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A sequential structure of statistical manifolds on deformed exponential family
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Frank Nielsen and Richard Nock · 2018
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