DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_79

Video : http://www.youtube.com/watch?v=hGc1z8EYR24

Slides: Matsuzoe-generalization independence Student.pdf

Presentation : https://www.see.asso.fr/node/14272

Creative Commons Attribution-ShareAlike 4.0 International

Abstract:

In anomalous statistical physics, deformed algebraic structures are important objects. Heavily tailed probability distributions, such as Student’s t-distributions, are characterized by deformed algebras. In addition, deformed algebras cause deformations of expectations and independences of random variables. Hence, a generalization of independence for multivariate Student’s t-distribution is studied in this paper. Even if two random variables which follow to univariate Student’s t-distributions are independent, the joint probability distribution of these two distributions is not a bivariate Student’s t-distribution. It is shown that a bivariate Student’s t-distribution is obtained from two univariate Student’s t-distributions under q-deformed independence.

DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_78

Video : http://www.youtube.com/watch?v=IpvuWcxHX4M

Slides: Sei_Geometric Properties textile plot.pdf

Presentation : https://www.see.asso.fr/node/14271

Creative Commons Attribution-ShareAlike 4.0 International

Abstract:

The textile plot proposed by Kumasaka and Shibata (2008) is a method for data visualization. The method transforms a data matrix in order to draw a parallel coordinate plot. In this paper, we investigate a set of matrices induced by the textile plot, which we call the textile set, from a geometrical viewpoint. It is shown that the textile set is written as the union of two differentiable manifolds if data matrices are restricted to be full-rank.

DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_77

Video : http://www.youtube.com/watch?v=8ePQ4NKTG-A

Slides: Mahammad-Djafari_variational Bayesian approximation.pdf

Presentation : https://www.see.asso.fr/node/14270

Creative Commons Attribution-ShareAlike 4.0 International

Abstract:

Clustering, classification and Pattern Recognition in a set of data are between the most important tasks in statistical researches and in many applications. In this paper, we propose to use a mixture of Student-t distribution model for the data via a hierarchical graphical model and the Bayesian framework to do these tasks. The main advantages of this model is that the model accounts for the uncertainties of variances and covariances and we can use the Variational Bayesian Approximation (VBA) methods to obtain fast algorithms to be able to handle large data sets.

DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_76

Video : http://www.youtube.com/watch?v=BPkO4sDSeE4

Slides: Brigo_Stochastic PDE projection.pdf

Presentation : https://www.see.asso.fr/node/14269

Creative Commons Attribution-ShareAlike 4.0 International

Abstract:

We review the manifold projection method for stochastic nonlinear filtering in a more general setting than in our previous paper in Geometric Science of Information 2013. We still use a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic partial differential equation for the optimal filter onto a finite dimensional exponential or mixture family, respectively, with two different metrics, the Hellinger distance and the L2 direct metric. This reduces the problem to finite dimensional stochastic differential equations. In this paper we summarize a previous equivalence result between Assumed Density Filters (ADF) and Hellinger/Exponential projection filters, and introduce a new equivalence between Galerkin method based filters and Direct metric/Mixture projection filters. This result allows us to give a rigorous geometric interpretation to ADF and Galerkin filters. We also discuss the different finite-dimensional filters obtained when projecting the stochastic partial differential equation for either the normalized (Kushner-Stratonovich) or a specific unnormalized (Zakai) density of the optimal filter.