# 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.

**3**

**1**answer

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

**0**

**0**answers

### Manifold structure of Gaussian mixtures

**1**

**0**answers

### Bounding the total variation metric between Gaussian mixtures

**2**

**0**answers

### Inequality on the Kullback-Leibler divergence

**0**

**0**answers

### Relation between the covariance of a random variable taking values in an embedded submanifold and the covariance matrix in the ambient Euclidean space

**5**

**1**answer

### Pythagorean theorems for other distances

**1**

**0**answers

### Connecting Wasserstein distance with mutual information?

**1**

**1**answer

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

**3**

**3**answers

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

**2**

**0**answers

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

**11**

**0**answers

### Relation between information geometry and geometric deep learning

**2**

**1**answer

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

**4**

**1**answer

### Convexity of exponential family

**2**

**0**answers

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

**1**

**0**answers

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

**1**

**0**answers

### Jensen-Shannon Divergence of Sample Distributions

**6**

**2**answers

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

**3**

**1**answer

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

**6**

**5**answers

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

**2**

**0**answers

### Parametric distances on product spaces of measures

**3**

**0**answers

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

**2**

**1**answer

### Is Bregman divergence independent of coordinates?

**3**

**0**answers

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

**3**

**0**answers

### Partial information decomposition for tangle machines

**2**

**0**answers

### Minimizer of a class of SDEs

**2**

**1**answer

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

**2**

**1**answer

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

**4**

**2**answers

### About optimization with Renyi divergence

**1**

**0**answers

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

**36**

**1**answer