November 18, 2009, 9:45, seminar room IMS, Goldschmidtstraße 7, 37077 Göttingen

Professor Christian Berg, University of Copenhagen

Some recent results about Student t-distributions

Abstract

The student t-distribution is a well-known infinitely divisible distribution with heavy tails. In this talk I will review some recent results about these distributions obtained in collaboration with Christophe Vignat from University of Marne la Vallee, France.

November 26, 2009, 16:15 seminar room 8.163, Blue Tower

José María Sarabia, Department of Economics, University of Cantabria, Santander, Spain

Multivariate GB2 Income Distributions

Abstract

The general beta of the second kind distribution (GB2) is a flexible distribution which includes several important and well-known distributions. This distribution has important applications in income and insurance studies. In this presentation three kinds of multivariate versions of the GB2 distribution are proposed. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables, where a hierarchy of distributions is presented. Several properties of these models are obtained. The second type of multivariate versions are based on a representation in terms of the log-logistic distribution. The third kind of models are based on conditional specification, where several classes are proposed and studied.

November 27, 2009, 09:00, NAM MN 68, Lotzestr, 16 - 18

Prof. Jean-Philippe Vert, Mines ParisTech Universität

Collaborative filtering in Hilbert spaces with spectral regularization

Abstract

Collaborative Filtering (CF) refers to the task of learning preferences of customers for products, such as books or movies, fr om a set of known preferences. More formally, this can be seen as the task of filling missing entries in a matrix where some entries are known. A standard approach to CF is to find a low rank approximation to the matrix. This problem is computationally difficult and some authors have proposed recently to search instead for a low trace norm matrix, which results in a convex optimization problem. We generalize this approach to the estimation of a compact operator, of which matrix estimation is a special case. We develop a notion of spectral regularization which captures both rank constraint and trace norm regularization, as well as many others. The major advantage of this approach is that it provides a natural method of utilizing side-information, such as age and gender, about the customers (or objects) in question - a formerly challenging limitation of the low-rank approach. We provide a number of algorithms, and test our results on a standard CF dataset with promising results. This is a joint work with Jacob Abernethy (UC Berkeley), Francis Bach (INRIA), and Theodoros Evgeniou (INSEAD).

talks at institutes & former ones