Results 11 to 20 of about 30,962 (265)
Immersions into Statistical Manifolds
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2021 This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then we obtain conditions for realizing an n-dimensional statistical manifold in an (n+1)-dimensional statistical manifold and ...
T. V. Mahaesh +1 more
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International Electronic Journal of Geometry, 2021 In this paper, we study the statistical immersion of codimension one from a Sasakian statistical manifold of constant φ− curvature to a holomorphic statistical manifold of constant holomorphic curvature and its converse. We prove that in both cases the constant φ− curvature equals to one and the constant holomorphic curvature must be zero. Moreover, we
Feng Wu, Yan Jıang, Liang Zhang
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Domain Adaptation on the Statistical Manifold [PDF]
2014 IEEE Conference on Computer Vision and Pattern Recognition, 2014 In this paper, we tackle the problem of unsupervised domain adaptation for classification. In the unsupervised scenario where no labeled samples from the target domain are provided, a popular approach consists in transforming the data such that the source and target distributions become similar.
Mahsa Baktashmotlagh +3 more
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Entropic Dynamics on Gibbs Statistical Manifolds [PDF]
Entropy, 2021 Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution.
Pedro Pessoa +2 more
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Biconnection gravity as a statistical manifold
Physical Review D, 2023 16 pages, no ...
Damianos Iosifidis +1 more
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Quantum Statistical Manifolds [PDF]
Entropy, 2018 Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum ...
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Laplacian operator on statistical manifold
Information Geometry, 2022 In this paper, we define a Laplacian operator on a statistical manifold, called the vector Laplacian. This vector Laplacian incorporates information from the Amari-Chentsov tensor. We derive a formula for the vector Laplacian. We also give two applications using the heat kernel associated with the vector Laplacian.
Ruichao Jiang +2 more
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Manifold Statistics for Essential Matrices [PDF]
, 2012 Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been shown to exhibit improved efficiency and accuracy. The
Dubbelman, G., Dorst, L., Pijls, H.
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Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds
Entropy, 2016 We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and
Stefan Sommer
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Manifold-adaptive dimension estimation revisited [PDF]
PeerJ Computer Science, 2022 Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it ...
Zsigmond Benkő +8 more
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