Max-linear models on directed acyclic graphs

Datum

18.05.2017

Zeit

17:00 - 18:00

Sprecher

Prof. Dr. Claudia Klüppelberg

Zugehörigkeit

TU München, Lehrstuhl für Mathematische Statistik

Serie

TUD Dresdner Mathematisches Seminar

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. A. Behme

Beschreibung

Graphical models are a popular tool to analyze and visualize dependence properties between random variables; see e.g. Lauritzen (1996). Each node in the graph represents a random variable, and the absence of an edge between two nodes indicates conditional independence between the corresponding random variables. We focus on directed graphical models, where edge orientations come along with an intuitive causal interpretation. We introduce a new recursive structural equation model, where all random variables can be written as a max-linear function of their parents and independent noise terms. We characterise all max-linear models, which are generated by a structural equation model and detail the relation between the coefficients of the structural equation model (the edge weights of the graph) and the max-linear coefficients. In particular, we show that the max-linear coefficient matrix is the solution of a fixed point equation. Max-weighted paths play an important role in the model, and we us this concept to derive minimal representations of the random vector components. This is joint work with Nadine Gissibl and based on the paper Gissibl, N. and Klüppelberg, C. (2015) Max-linear models on directed acyclic graphs. Available at: http://arxiv.org/pdf/1512.07522v1.pdf

Letztmalig verändert: 03.05.2017, 09:59:45