Max-linear models on graphs
Date/Time:23 May 2018 10:30
Venue: S17 #04-06 SR1
Speaker: Claudia Klüppelberg, Technical University of Munich
Max-linear models on graphs
Graphical models are a popular tool to analyse and visualise 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 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 variables.
In particular, we define directed graphical models, where edge orientations come along with an intuitive causal interpretation and present conditional independence properties of the model. Furthermore, we use algebraic methods to 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. Finally, we extend finite-dimensional max-linear models to models on infinite graphs, and investigate their relations to classical percolation theory, more precisely to nearest neighbour Bernoulli bond percolation. The talk is based on joint work with Nadine Gissibl, Steffen Lauritzen, Moritz Otto, and Ercan Sönmetz.
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