estrange
发表于 2025-3-21 18:25:04
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斗争
发表于 2025-3-21 20:27:14
https://doi.org/10.1007/978-4-431-55978-8Dual differential geometry; Information geometry; Machine learning; Mathematical neuroscience; Natural g
食物
发表于 2025-3-22 03:12:04
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HERTZ
发表于 2025-3-22 04:41:27
Invariant Geometry of Manifold of Probability DistributionsWe have introduced a dually flat Riemannian structure in the manifolds of the exponential family and the mixture family based on the convexity of the cumulant generating function (free energy) and the negative entropy, respectively. The KL-divergence is derived from these convex functions.
ascetic
发表于 2025-3-22 09:12:57
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不遵守
发表于 2025-3-22 13:11:31
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保守
发表于 2025-3-22 17:18:38
Dual Affine Connections and Dually Flat ManifoldWe have considered one affine connection, namely the Levi–Civita connection, in a Riemannian manifold .. However, we can establish a new edifice of differential geometry, by treating a pair of affine connections which are dually coupled with respect to the Riemannian metric.
可行
发表于 2025-3-22 22:25:14
Asymptotic Theory of Statistical InferenceLet . be a statistical model specified by parameter ., which is to be estimated.
关节炎
发表于 2025-3-23 02:51:45
Estimation in the Presence of Hidden VariablesLet us consider a statistical model ., where vector random variable . is divided into two parts . so that .. When . is not fully observed but . is observed, . is called a hidden variable.
Pde5-Inhibitors
发表于 2025-3-23 05:50:27
Neyman-Scott Problem: Estimating Function and Semiparametric Statistical ModelThe present chapter studies the famous Neyman–Scott problem, where the number of unknown parameters increases in proportion to the number of observations.