Bayesian Neighbourhood Estimation
Project funded by own resources
Project title Bayesian Neighbourhood Estimation
Principal Investigator(s) Roth, Volker
Project Members Keller, Sebastian Mathias
Wieczorek, Aleksander
Kaufmann, Dinu
Organisation / Research unit Departement Mathematik und Informatik / Datenanalyse (Roth)
Project start 01.06.2015
Probable end 31.12.2018
Status Active

In this project, we take a Bayesian perspective of estimating the neighbourhood of a set of p query variables in
an undirected network of dependencies. Gaussian Graphical Models (GGM) are a tool for repre-
senting such relationships in an interpretable way. In a classical GGM setting, the sparsity pattern
of the inverse covariance matrix W encodes conditional independence between variables of the
graph. Consequently, various estimators have been proposed that reduce the number of parameters
by imposing sparsity constraints on W, e.g. the graphical lasso procedure and its Bayesian
extensions. We consider a sub-network corresponding to the neighbourhood of a set of query
variables, where the set of potential neighbours is big. We aim at developing an efficient inference scheme
such that the estimation of the sub-network is possible without inferring the entire network.

In real world situations it is often the case that we have to estimate a full network but interpret only
part of it. An example of such a situation is modelling the dependence between clinical variables
and a potentially large set of genetic explanatory variables. Here, we would be more interested in
establishing the links between these portions, rather than examining the links within the portions
themselves. The proposed idea averts prohibitive computations on the whole network and makes
it possible to estimate only the parts of interest. An additional challenge is the ability to handle
missing values and heterogenous data, i.e. continuous and discrete random variables at the same
time. We plan to achieve this by a copula extension.

Keywords Archetypal Analysis
Financed by University funds

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