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Multiscale SPD manifold learning for rehabilitation exercise evaluation. [PDF]
Sci RepBai Z +6 more
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Exponential statistical manifold
Annals of the Institute of Statistical Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CENA A, PISTONE, Giovanni
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Musical Isomorphisms and Statistical Manifolds
Mediterranean Journal of Mathematics, 2022On a pseudo-Riemannian manifold \((M, g)\), an affine connection \(\nabla\) is called a Codazzi connection if \(\nabla g\) is totally symmetric. The triple \((M,g,\nabla)\) is called a statistical manifold if \(\nabla\) is torsion free and Codazzi. This is the setting of information geometry.
Esmaeil Peyghan +2 more
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Information geometry and statistical manifold
Chaos, Solitons & Fractals, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdel-All, Nassar H. +2 more
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Statistical manifolds are statistical models
Journal of Geometry, 2006In this note we prove that any smooth (C1 resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get positive answers to Lauritzen´s question and Amari´s question on a realization of smooth (C1 resp.) statistical manifolds as finite dimensional statistical models.
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Diffusion Kernels on Statistical Manifolds
1999A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian kernel of Euclidean space.
Lafferty, John D., Lebanon, Guy
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