—– ANNULÉ —–
DATE : Le vendredi 27 février 2009
CONFERENCIER : Sayan Mukherjee (Duke University)
TITRE : Two representations of graphical models
LIEU : UQAM, 201, ave Président Kennedy, Salle PK-5115
HEURE : 15 h 30
In this talk I will discuss two problems: decomposition of gene networks and inference of conditional dependencies.
The first part of the talk describes a method to decompose pathways or gene networks into sub-networks and infer the relevance of these sub-components in explaining phenotypic variation. The approach which we call multiscale graphical models is strongly related to old ideas such as path analysis. Specifically, it is based on the idea of diffusion wavelets which in our application is a multiscale decomposition of a partial correlation matrix or the generator of a Markov chain. We describe results on yeast gene expression data to illustrate the method and then provide preliminary data on prostate cancer.
The second part of the talk formulates a novel approach to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, an informative prior distribution is placed over decomposable graphs and the induced posterior distribution is sampled. The key idea developed is a parametrization of decomposable hypergraphs using the geometry of points in Euclidean space. This allows for specification of informative priors on decomposable graphs by priors on a finite set of points. This construction has been well studied in the fields of computational topology and random geometric graphs.
Joint work with Justin Guinney, Simon Lunagomez, Mauro Maggioni, Robert Wolpert, and Phillip Febbo