Thursday, June 19, 2014

Randomized Comments: Code for GWAS and CS study, a new blog, Geometric theory of information

... There will be a "before" and "after" this paper ..., I mentioned that my review could be found starting at page 4 of this author's comment. If you read this response from the author, you'll note the location of the GitHub repository for the solver used in the paper. It is made available by the authors thanks to the request made in the review and it is here:

check the section  'compressed sensing; scripts for "Applying compressed sensing to genome-wide association studies"'

Pierre Vandergheynst has a blog and his first entry is on his upcoming course on Harmonic analysis on graphs and networks.

The foundation of all these geometries is given by hessian geometry of Jean-Louis Koszul. The important concept is the Koszul-Vinberg Characteristic function. By selecting the inner product deduced from Cartan-Killing form, we recover the good geometry of covariance matrix.
This idea has been extended by Jean-Marie Souriau in statistical physics, where the metric is introduced through symplectic cocycle, proving that the metric is invariant by dynamic groups in physics.
Entropy could be introduced by Legendre transform of minus the logarithm of Koszul-Vinberg characteristc function.
I have recently developed these Koszul and Souriau works in a long paper published in Springer book "geometric theory of information" edited by Frank Nielsen (also on Google Books)

This paper also deals with quantum Fisher metric introduced by Roger Balian in 1986. Another paper Will be published soon in MDPI journal "Entropy" with title "Koszul Information Geometry and Geometric Temperature/Capacity of Souriau Lie Group Thermodynamics".
For MaxEnt'14, a special issue will be published in MDPI Journal "entropy": Entropy, Information and their Geometric Structures
Frédéric Barbaresco
Thanks Frédéric

[1] and [2] have same idea. [1] using a fixed threshold, while [2] using a weight process. In [2], there are some difference between implementation and presentation. I don't like this :)).

Then Zaidao Wen mentioned

Maybe a smoothed idea of logdet or related has been involved in "Generalized Nonconvex Nonsmooth Lowrank Minimization" CVPR2014

Image Credit: NASA/JPL-Caltech
This image was taken by Navcam: Left B (NAV_LEFT_B) onboard NASA's Mars rover Curiosity on Sol 664 (2014-06-19 09:28:28 UTC).
Full Resolution

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