Information geometry

October 21, 2011 — December 27, 2019

functional analysis
Figure 1

A placeholder for a particular type of learning on curved spaces about which I do not in fact know anything.

Maybe see Azimuth’s Information Geometry Series plus the overview

1 References

Amari, Shunʼichi. 1987. “Differential Geometrical Theory of Statistics.” In Differential Geometry in Statistical Inference.
Amari, Shun-ichi. 1998. Natural Gradient Works Efficiently in Learning.” Neural Computation.
Amari, Shunʼichi. 2001. Information Geometry on Hierarchy of Probability Distributions.” IEEE Transactions on Information Theory.
Amari, Shun-ichi, Karakida, and Oizumi. 2018. Fisher Information and Natural Gradient Learning of Random Deep Networks.” arXiv:1808.07172 [Cond-Mat, Stat].
Amari, Shun-ichi, Park, and Fukumizu. 2000. Adaptive Method of Realizing Natural Gradient Learning for Multilayer Perceptrons.” Neural Computation.
Ay. 2002. An Information-Geometric Approach to a Theory of Pragmatic Structuring.” The Annals of Probability.
Barndorff-Nielsen. 1987. “Differential and Integral Geometry in Statistical Inference.” In Differential Geometry in Statistical Inference.
Brody, and Rivier. 1995. Geometrical Aspects of Statistical Mechanics.” Phys. Rev. E.
Caticha. 2015. The Basics of Information Geometry.” In.
Csiszár. 1975. I-Divergence Geometry of Probability Distributions and Minimization Problems.” The Annals of Probability.
Doyle, and Steiner. 2011. Commuting Time Geometry of Ergodic Markov Chains.”
Fernández-Martínez, Fernández-Muñiz, Pallero, et al. 2013. From Bayes to Tarantola: New Insights to Understand Uncertainty in Inverse Problems.” Journal of Applied Geophysics.
Kass, Amari, Arai, et al. 2018. Computational Neuroscience: Mathematical and Statistical Perspectives.” Annual Review of Statistics and Its Application.
Khan, and Zhang. 2022. When Optimal Transport Meets Information Geometry.” Information Geometry.
Kulhavý. 1990. Recursive Nonlinear Estimation: A Geometric Approach.” Automatica.
Lauritzen. 1987. “Statistical Manifolds.” In Differential Geometry in Statistical Inference.
Ly, Marsman, Verhagen, et al. 2017. A Tutorial on Fisher Information.” Journal of Mathematical Psychology.
Mallasto, Gerolin, and Minh. 2021. Entropy-Regularized 2-Wasserstein Distance Between Gaussian Measures.” Information Geometry.
Martens. 2020. New Insights and Perspectives on the Natural Gradient Method.” Journal of Machine Learning Research.
Miolane, Mathe, Donnat, et al. 2018. Geomstats: A Python Package for Riemannian Geometry in Machine Learning.” arXiv:1805.08308 [Cs, Stat].
Mosegaard, and Tarantola. 1995. Monte Carlo Sampling of Solutions to Inverse Problems.” Journal of Geophysical Research: Solid Earth.
———. 2002. Probabilistic Approach to Inverse Problems.” In International Geophysics.
Nielsen. 2018. An Elementary Introduction to Information Geometry.” arXiv:1808.08271 [Cs, Math, Stat].
Palomar, and Verdu. 2008. Lautum Information.” IEEE Transactions on Information Theory.
Poole, Lahiri, Raghu, et al. 2016. Exponential Expressivity in Deep Neural Networks Through Transient Chaos.” In Advances in Neural Information Processing Systems 29.
Raginsky, and Sason. 2012. Concentration of Measure Inequalities in Information Theory, Communications and Coding.” Foundations and Trends in Communications and Information Theory.
Transtrum, Machta, and Sethna. 2011. The Geometry of Nonlinear Least Squares with Applications to Sloppy Models and Optimization.” Physical Review E.