Titlebook: Information Geometry and Its Applications; On the Occasion of S Nihat Ay,Paolo Gibilisco,František‘Matúš Conference proceedings 2018 Spring

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做作

Information Geometry and Game Theoryelvey and Palfrey. Here, the players are assigned parameters measuring their degree of rationality, and the resulting equilibria are Gibbs type distribution. This brings us into the realm of the exponential families studied in information geometry, with an additional structure arising from the relat

残废的火焰

Higher Order Equivalence of Bayes Cross Validation and WAICo the widely applicable information criterion (WAIC), even if the posterior distribution can not be approximated by any normal distribution. In the present paper, we prove that they are equivalent to each other according to the second order asymptotics, if the posterior distribution can be approxima

蹒跚

Restricted Boltzmann Machines: Introduction and Reviewas popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Boltzmann machines carry a rich structure, with connections to geometry, applied algebra, probability, statistics, machine learning, a

absorbed

Congruent Families and Invariant Tensorsent Markov morphisms is the Fisher metric and the only invariant 3-tensor field is the Amari–Chentsov tensor. We generalize this result for arbitrary degree ., showing that any family of .-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor

爱管闲事

Nonlinear Filtering and Information Geometry: A Hilbert Manifold Approachions” process. Nonlinear filters are typically represented in terms of stochastic differential equations for the posterior distribution of the signal. The natural “state space” for a filter is a sufficiently rich family of probability measures having a suitable topology, and the manifolds of infinit

Rebate

Infinite-Dimensional Log-Determinant Divergences III: Log-Euclidean and Log-Hilbert–Schmidt Divergenan distance as a special case. This is then generalized to a family of Log-Det divergences on the set of positive definite Hilbert–Schmidt operators on a Hilbert space, with the Log-Hilbert–Schmidt distance being a special case. The divergences introduced here are novel both in the finite and infini

Geyser

Palpitation

Information Geometry Associated with Generalized Meansodesic and m-geodesic, which associates with the canonical divergence and generalized expectation. The generalized e-geodesic is given by Kolmogorov–Nagumo means; the generalized m-geodesic is characterized to preserve the generalized expectation. The Pythagorean theorem with respect to the canonica

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