information geometry

As a starting point for understanding duality in projective geometry, we first recall the axioms defining a general projective plane ...

mathematicalgemstones.com·629.5 KB

Information geometry gives a powerful method to information sciences and physics based on the dual structure of affine connections. It is rather surprising ...

bsi-ni.brain.riken.jp·597.6 KB

Among the proposed measures, one of the best known is the I directed divergence [17], [19] or its symmetrized measure, the J divergence. Although the I and J ...

www.cise.ufl.edu·560.8 KB

Those statistical patterns are interpreted and handled geometrically in statistical manifolds either as single points, weighted sparse point sets or non- ...

www.lix.polytechnique.fr·504.9 KB

The present article extends the notation of topological statistical models by a differential structure to statistical manifolds and introduces ...

arxiv.org·468.1 KB

A statistical manifold is an extension of a Riemannian manifold. ... In section 4, we define golden statistical manifolds to prove the condition for the ...

tensorsociety.com·446.3 KB

Although often not explicitly stated, gradient descent is most useful for cost functions (i) that have a single mini- mum and (ii) whose gradients are isotropic ...

www.yaroslavvb.com·402.9 KB

Divergence-measure fields are extended vector fields, including vector fields in Lp and vector-valued Radon measures, whose divergences are. Radon measures.

people.maths.ox.ac.uk·396.8 KB

Divergence-measure fields have been investigated by several authors and we refer the readers to the papers Chen-Frid [7, 8], Chen-Torres [9], Chen-Torres-.

www.math.purdue.edu·350.2 KB

The present paper shows how information geometry gives an answer to the problem of invariant decomposition for hi- erarchical systems of probability ...

qwone.com·339.9 KB

This paper presents a unifying view of message- passing algorithms, as methods to approximate a complex Bayesian network by a simpler network.

groups.seas.harvard.edu·331.0 KB

This gives path geometry on surfaces as we now understand it and the duality is the classical duality of second order differential equations. Namely, one ...

sites.math.duke.edu·303.7 KB

Density estimation requires introducing relevant measures of divergence between probability densities that we can compute e ciently. Historically many ...

danilorezende.com·300.1 KB

The duality principle in projective geometry seems to have been stated for the first time in full generality by J.D. Gergonne.

thomasedwardforster.github.io·267.7 KB

The duality principle in projective geometry seems to have been stated for the first time in full generality by J.D. Gergonne.

www.dpmms.cam.ac.uk·267.7 KB

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the param- eter space.

homes.cs.washington.edu·218.6 KB

The link between measures of uncertainty and imprecision in fuzzy environments will lie in what we will refer as divergence measure, because of the analogy with ...

digibuo.uniovi.es·206.5 KB

Logical duality would lead to inver- sion of order structures such as lattices, and there merge with similar ideas coming from projective geometry. Pontrjagin ...

ncatlab.org·206.1 KB

Duality in mathematics is not a theorem, but a “principle”. It has a simple origin, it is very powerful and useful, and has a long history going.

fme.upc.edu·188.1 KB

In geometry, the platonic solids have a duality between each other. The cube and octahedron are dual, while the dodecahedron and icosahedron are dual. The ...

math.berkeley.edu·133.1 KB