Differential Geometry of Curved Exponential Families-Curvatures and Information Loss

By Shun-ichi Amari. 1982

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, methodology): “This is the inverse Riemannian metric and the inverse Fisher information matrix (Amari 1982).”
Objective Priors: An Introduction for Frequentists (2011, unknown): “Next, back to the one-parameter case, we consider the more general distance (Amari, 1982; Cressie and Read, 1984) Dπ = [ 1−E { π(θ”
Scalable Inference of Overlapping Communities (2012, unknown): “4 can be rewritten using ∑ a,bEq[log p(yab|za→b, za←b,β)] = Eh[ 1 c 1 h(t) ∑ (a,b)∈st Eq[log p(yab|za→b, za←b,β)]] (8) (2)Stochastic variational inference uses natural gradients [19] of the ELBO.”
Stochastic variational inference (2012, methodology): “Amari (1998) showed that we can compute the natural gradient by premultiplying the gradient by the inverse of the Riema nnian metricG(λ)−1, ∇̂λ f (λ), G(λ)∇λ f (λ), whereG is the Fisher information matrix of q(λ) (Amari, 1982; Kullback and Leibler, 1951), G(λ) = Eλ [”
Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching (2003, methodology): “Finally, it is worthwhile to note the connection be-tween the approximate methods described in this paper, and the classical Legendre duality between the negative entropy function and the log partition function [1, 6].”
Exponential statistical manifold (2007, methodology): “in Amari (1982) , Amari (1985), Amari and Nagaoka (2000), with the specification that we want to construct a Banach manifold structure in the classical sense, see e.g.”
Graphical Models, Exponential Families, and Variational Inference (2008, background): “In our view, the most promising avenue towards variational methodology tuned to statistics is to build on existing links between variational analysis and the exponential family of distributions [3, 5, 17, 35].”
Information geometry and sufficient statistics (2012, background): “Moreover, there exists a natural affine structure on spaces of probability measures as discovered by Amari [1,2] and Chentsov [15].”