Special Issue:Information Geometry and Its Applications Preface .......... Shun-ichi Amari and Shiro Ikeda (59, 1-2) A modified EM algorithm for mixture models based on Bregman divergence .......... Yu Fujimoto and Noboru Murata (59, 3-25) Exponential statistical manifold .......... Alberto Cena and Giovanni Pistone (59, 27-56) A new algorithm of non-Gaussian component analysis with radial kernel functions .......... Motoaki Kawanabe, Masashi Sugiyama, Gilles Blanchard and Klaus-Robert Müller (59, 57-75) The geometry of proper scoring rules .......... A. P. Dawid (59, 77-93) Extending local mixture models .......... Paul Marriott (59, 95-110) Local mixtures of the exponential distribution .......... K.A. Anaya-Izquierdo and P. K. Marriott (59, 111-134) Bayesian prediction based on a class of shrinkage priors for location-scale models .......... Fumiyasu Komaki (59, 135-146) Uncertainty principle and quantum Fisher information .......... Paolo Gibilisco and Tommaso Isola (59, 147-159) A note on curvature of \alpha-connections of a statistical manifold .......... Jun Zhang (59, 161-170)

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ETVC08

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To conclude, let us mention that Albert Robida also wrote and illustrated the book "The Electric Life" where he depicts life in the 20th century and warns mankind of the potential danger of using non-controlled technology. How timely! We're all now fully aware and have imminently to face this issue.

Frank Nielsen.

A few links:.

A short biography:.

http://en.wikipedia.org/wiki/Albert_Robida

Robida's "Twentieth Century" book:.

http://www.amazon.com/Twentieth-Century-Classics-Science-Fiction/dp/0819566802/ref=sr_1_1?ie=UTF8&s=books&qid=1208178705&sr=1-1

History of the first recorded sound:.
http://www.firstsounds.org/

Generalized Kullback-Leibler (positive measures):

Itakura-Saito (Burg entropy):

Logistic loss:

To create the STL files, you need to discretize the surface of theses balls by walking on their geodesics passing through the centers. A bisection search does this to stop a more or less the radius.

Robida ????????????????????????1883????????? ? "phonoscope" ????????????? "phonoscope" ?????????????????????????????????? 1879?? Edison ? "telephonoscope" ?????????????????????????????????????????????????????????????????Robida ??? "e-?????" ???????????? ?????????????????????????????????????? ... WALKMAN ??????????????????? (a walk man) ?????????????????????????????????????????????????????????????????????????? ... ?????????????????????????????????????????????????? ????????????????????? (2008?3?) ??????????????? Edouard-Leon Scott de Martinville ? 1860 ?4?9???????????? Au Clair de la Lune ?????????? ??????????Scott ???? 1857?????? phonautographic ????????????????????? (INPI) ?????????????????????????????????????????????????????? ?????????? ?????????????????(??????????????) ??????????????????? (???? Edison ?1927????????????????????????????)

??? Albert Robida ????????? "The Electric Life" ??????????????? 20???????????????????????????????????????????????????? ...

Frank NIELSEN, excerpts 2008.

Registration is now open (and free)

ETVC08

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Error Analysis of a Numerical Calculation about One-qubit Quantum Channel Capacity (ISVD'07)

investigates the numerical error in computing the Holevo channel capacity using the furthest Voronoi diagram wrt. to the von Neuman quantum divergence. They show that the error is in O(1/eps) for sampling in the latitude-longitude 1/eps points.

This algorithm allows us to study, e.g., the additivity conjecture of quantum channels.

It is a nice aspect of quantum information geometry derived from traditional computational geometry. Interestingly, the Legendre transformation for 1-qubit represented on the Bloch sphere is explicited too.

Read the ranking

Pages: 195 - 200
Year of Publication: 2002 ISSN:1230-1612

The authors rise and solve the following question:
Does any Riemannian manifold (M,g) admits a dually flat structure on M (ie, a pair of dually torsion-free connections) ?
The answer is no (eg., compact Riemannian manifolds with finite fundamental group, independent of the metric: this is a purely topological argument). Then the authors go one on finding the conditions for such an existence by considering pair of connections with at least one of them complete, meaning that the geodesics are defined on the whole real line. In probabilistic information geometry, it is the case for the exponentia connection nabla^(e) but the mixture connection nabla^(m) is not complete creating a full range of optimization problems involving Bregman projections. Finally, applications to quantum information geometry is reported. This is a well-written paper that focuses on global topological property of dual flatness, a must-read that I recommend.

The short paper (always good) gives an executive view of how to use the Fisher-Rao metric to compute shape geodesics using mixture models (like GMMs).

They apply their method on 2D corpuse callosum shapes.

This is one important problem for building and comparing a shape repository with a shape atlas.

The geodesic is used to drive the deformation on the ambiant Euclidean space.

Thank you for letting me know of this work.

Another talk was about Clifford algebra (and geometric algebra interpretation). Here the basic primitive is not point but sphere and the vectors are splitted into 3 categories for inner products of basis equal to 1, -1, or 0. This seems to be a full generalization of the many anterior algebras. I am curious to hear about differential extensions of it. Tomorrow is the application day. Looking forward to hearing part II!

Tomorrow, I'll attend the COE workshop on math aspects of image processing and computer vision. I'm looking forward to hearing the talks.

Empirical development of an exponential probabilistic model for text retrieval: using textual analysis to build a better model

The authors concentrate on determining what is a good model for explaining a text corpus. They show that the multinomial model falls short, as it is widely known, and go on learning the 1-order exponential family that better represent corpora for naive Bayesian retrieval.

Overall, although we cannot explain all data sets, and risk over-fitting, it is crucial to design better generative models. One big success these years was the LDA (Latent Dirichlet Allocation) scheme. But, this has to be learnt and not hardcoded anymore. There is plenty room for this line of research...

I found by browsing the www the following paper:
THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS (1991)
I am amazed about the possibilities of studying things once they have an avatar point lying on an avatar world (ie: the differential manifold)

Batch and on-line parameter estimation of Gaussian mixtures based on the joint entropy

The authors compute the relative entropy (KL divergence) among two Gaussian mixture models (GMMs) and derive a simple update rule (in sec 5). They call their method joint entropy (JE) update and claim that it requires half the steps of the EM.

The important remark is to notice that the relative entropy between two GMMs is non-convex. So they proceed by studying an upper-bound called the joint entropy distance

Mutual-information-based registration of medical images: a survey (2003)

The definition given is just the sum of the marginal entropies over the joint-entropy

MIC Framework: An Information-Theoretic Approach to Quantitative Association Rule Mining

The authors present an efficient system for finding out quantitative association rules (QARs) by wise combinatorial enumeration in graph with edges built if and only if the corresponding vertices have a good normalized mutual information.

The normalized mutual information is defined as:

The paper makes mention of an article of Sergey Brin, that is well cited (over 150+) on citeseer. This paper defines a notion of interestingness of an association rule.

The question remains open to find out the geometry and axiomatic approach of defining good rules in data mining...

Empirical evaluation of dissimilarity measures for color and texture

The paper compares 9 kinds of divergences for several applications of computer vision such as classification supervised/unsupervised segmentation, and, image annotation and retrieval. I am not going to cite verbatim their concluding remarks, but for short (1) EMD is performing very good for partial matches, and (2) there is no winner for all tasks, which confort my point of view: divergences should be tailored and learnt from data-sets on the fly.
Also adaptive binning in histogram seems to be a key for improved performance.

Differential Entropic Clustering of Multivariate Gaussians.

The paper shows how to clustering a set of multivariate normals with respect to the Kullback-Leibler divergence. The key ingredient that makes it a non-trivial application of the former clustering with Bregman divergence paper (JMLR'05) is to show how to compute the centroid of a set of multivariate normals by decomposing the Bregman divergence into a convex sum of two Bregman divergences: a Mahalanobis distance on the means followed by a Burg matrix divergence on the variance-covariance matrix.

The authors also report on experimental results by using the normalized mutual information.

Ok, the Earth Mover Distance (EMD) distance introduced in 1997 by Stanford CS group, is in fact known to statisticians under the name of Mallows distance:

It coincides exactly for normalized histograms but not for unormalized distributions. I recommend reading ICCCV'01's paper for a nice description of these similitudes:
The Earth Mover's distance is the Mallows distance: some insights from statistics

Ok, I push the "preview" button and cross fingers for not encountering the same problem twice -:)

Efficient Shape Indexing Using an Information Theoretic Representation

Spellman and Vemuri presented a left-side KL minimax center for probability density functions belonging to the exponential families (using log-partition statistical physics notations).

They prove that the minimizer is unique and defines the e-radius

Finally, they show that the center allows more efficiency for nearest neighbor queries. There is definitively "something" information geometry to be done on barycenters and centroids, like Bruno Pelletier first initiated in his 2005 paper.