# Questions tagged [information-geometry]

Information geometry is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory. This is done by taking probability distributions for a statistical model as the points of a Riemannian manifold, forming a statistical manifold. The Fisher information metric provides the Riemannian metric.

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### Rotationally symmetric manifold with statistical structure

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### intuition about Gaussian processes over a finite space

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### Statistical manifolds with trivial statistical structure after quotienting

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### reverse KL-divergence: Bregman or not?

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### Parameterization of exponential family

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### Comparison of Information and Wasserstein Topologies

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### Complete statistical manifolds

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### Projections in infinite dimensional statistical manifolds

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### What is the correct notion of morphism between statistical manifolds?

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### Information monotonicity of divergence => function of $f$-divergence

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### From $f$-divergence to its dual: the transformation of convex functions on $\mathbb R_+$ by $f^*(t) = 1 f(\frac 1 t)$

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### Ideas on how to prove Pythagorean identity involving Wasserstein distances?

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### Smallest $\mathrm{D}(Q\|P)$ given fixed marginals $\mathrm{D}(Q_X\|P_X)$ and $\mathrm{D}(Q_Y\|P_Y)$

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### How to study to learn differential geometry for applying it to statistics

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### Which books should I read in order to be prepared to study information geometry?

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### Bounding the total variation metric between Gaussian mixtures

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### Inequality on the Kullback-Leibler divergence

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### Pythagorean theorems for other distances

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### Connecting Wasserstein distance with mutual information?

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### Does a 1-Lipschitz function preserve mutual information between two random variables?

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### Introduction to information geometry and/or geometric control theory

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### Is there any geometric interpretation for the trace of Fisher information matrix?

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### Relation between information geometry and geometric deep learning

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### Relationship between $\alpha$-divergences?

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### Convexity of exponential family

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### Variational inference: Does the natural gradient follow (Fisher-Rao) geodesics locally?

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### Binary search extension for determining a hyperplane splitting a set of points in $\mathbb{R}^d$

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### Jensen-Shannon Divergence of Sample Distributions

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### Approximation of Wasserstein distance between $p_\theta$ and $p_{\theta + d\theta}$

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### Interpolation inequality related to the 5/3-Laplace operator

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### Reviews of Probability in High Dimension not by Van Handel

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### Parametric distances on product spaces of measures

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### Distance measures that preserve Pythagoras' theorem but break the triangle inequality

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### Is Bregman divergence independent of coordinates?

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### Covariance operator analogue for manifolds and respective measure manifolds

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### Partial information decomposition for tangle machines

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### Minimizer of a class of SDEs

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### How much can KL divergence decrease by diluting the reference distribution

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### (quasi)metric on Riemannian manifolds via Brownian Motion?

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### About optimization with Renyi divergence

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### Relation between Aitchison Distance on a Simplex and Geodesic distance on the multinomial manifold [closed]

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