Johan van Horebeek

Modeling high dimensional binary data based on Interaction Graphs


Nowadays, Graphical Models constitute a popular approach to build
probabilistic models for high dimensional data. They make use of a
graph that represent (part of the) the conditional independency
structure.  Their success is partly attributable (1) to the ease of
working with and understanding of graphs acting as a intuitively clear
interface between the model/data and the user, (2) to the possibility
to incorporate a priori defined knowledge and (3) to the possibility
of formulating and deriving many properties in terms of properties of
the graph.  An often mentioned drawback of those models is that they
only provide a rough understanding of the underlying interaction
structure.

In this talk, we will study a class of graphs, called Interaction
Graphs, that allows us to describe and visualize the interaction
structure between binary multivariate characteristics at a finer scale
than what one obtains with Classical Models.  We investigate the
representation and consistency problem and how estimation of the
parameters can be done.  An application to web access data is briefly
discussed.