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pyBregMan: A Python library for geometric computing on BREGman MANifolds with applications. # Installation !pip install pyBregMan and check the readme example: github.com/alexandersoen/…

Paper by Prof Amari (1991) with quotes: "... [new unifying method to information sciences] to provide a new unifying method to information sciences.'' ``It opens a new field called information geometry.'' ``This papers opens a new fertile field of neural network research.''

Books with good synergies!

Must read retrospectively: "Mathematical foundations of neurocomputing. Proceedings of the IEEE 78.9 (1990): 1443-1463 by Professor Shun-ichi Amari. A tutorial and review back in 1990 with many figures... ieeexplore.ieee.org/document/58324/

Relative Fisher Information Matrix (RFIM) and Relative Natural Gradient (RNG) for deep learning

Visualizing Chernoff information as radii of primal and dual Bregman balls. tinyurl.com/s6rzwyu

Excellent book... with great title! 👍

Total Bregman divergences measures the convex gap by orthogonal projection to the tangent hyperplane rather than the "vertical" projection Properties: - invariant to rotations - yield provably robust clustering - tBD amounts to a conformal BD 👉 tinyurl.com/tBregDiv

A generalization of the Bhattacharyya distance using a pair of abstract means. Useful in statistics to get closed-form formula when handling non exponential families. arxiv.org/abs/1401.4788 Publisher: sciencedirect.com/science/articl…

Historically, the naming of certain concepts has not always been precise: The Bhattacharyya distance is not, strictly speaking, a mathematical distance, as it fails to satisfy the triangle inequality. It is a misnomer and should have been called the Bhattacharyya dissimilarity.

Fast approximation of the Löwner extremal matrices of high-dimensional symmetric matrices arxiv.org/abs/1604.01592

Definitively worth your time. Prof Gromov was invited speaker at MaxEnt 2014

Theorem #OTD: The expected Kullback-Leibler divergence between the true d-dimensional model and the model at the maximum likelihood estimate is d/(2n) (Under regularity condition) tinyurl.com/ElementaryIG extends to f-divergences... tinyurl.com/fdivTaylorChi