Advances in Statistical Modeling of High Dimensional Data:
Variable selection, and Challenges in Image Analysis

Ulrich Mansmann, LMU München

Indirect comparison of interaction graphs

A new approach to test differential conditional independence structure (CIS) in two graphs is introdoced. The two graphs have the same set of nodes and are estimated from data sampled under two different conditions. The statsitic uses the entire pathplot in a Lasso regression as the information how a node connects with the remaining nodes in the graph. Interpreting its paths as random processes allows defining stopping times which make the statistical properties of the test statistic accessible to analytic reasoning. A resampling approach will be used to calculated p-values simultaneously for a hierarchical testing procedure. The hierarchical testing steps through a given hierarchy of clusters. First, collective effects are measured at the coarsest level possible (the global null hypothesis that no node in the graph shows a differential CIS). If the global null hypothesis can be rejected, finer resolution levels are tested for an effect until the level of individual nodes is reached. The approach can be applied to problems in moldecular medicine as well as to complex phenotypes as presented for example by the International Classification of Functioning (ICF).

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