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Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification. [PDF]
J Sci ComputZanoni A +4 more
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Multiscale SPD manifold learning for rehabilitation exercise evaluation. [PDF]
Sci RepBai Z +6 more
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Representational learning by optimization of neural manifolds in an olfactory memory network
Friedrich R +7 more
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Musical complexity governs a tradeoff between reliability and dimensionality in the neural code
Mouawad PG +3 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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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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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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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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