# Information Geometry and Classical Cram'er-Rao Type Inequalities

arXiv: https://arxiv.org/abs/2104.01061 · HTML: https://mlsanity.com/paper/2104.01061/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 85 references that are in the map.
- First posted on arXiv 2 Apr 2021.

## Builds on (most cited first, 4 of 4)

- [Natural Neural Networks](https://mlsanity.com/paper/1507.00210/) (2015)
- [Quantum query complexity of entropy estimation](https://mlsanity.com/paper/1710.06025/) (2017)
- [Generalized Bayesian Cram'er-Rao Inequality via Information Geometry of Relative α-Entropy](https://mlsanity.com/paper/2002.04732/) (2020)
- [Spontaneous Clustering via Minimum γ-divergence](https://mlsanity.com/paper/1304.7867/) (2013)

## Built on by (most cited first, 1 of 1)

- [Information Geometry for the Working Information Theorist](https://mlsanity.com/paper/2310.03884/) (2023)

## Abstract (arXiv)

We examine the role of information geometry in the context of classical Cram'er-Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying Amari-Nagoaka's theory to obtain a CR type inequality. The classical deterministic CR inequality is derived from Kullback-Leibler (KL)-divergence. We show that this framework could be generalized to other CR type inequalities through four examples: α-version of CR inequality, generalized CR inequality, Bayesian CR inequality, and Bayesian α-CR inequality. These are obtained from, respectively, Iα-divergence (or relative α-entropy), generalized Csisz'ar divergence, Bayesian KL divergence, and Bayesian Iα-divergence.