Concentration and covariance graphs are two of the widely studied classes of graphical models.
These models are often constructed through pairwise relationships between the variables of a given random vector. Concentration graphs are constructed from conditional independencies, whereas covariance graphs are constructed from marginal independencies. Under suitable conditions, more complex conditional independence relationships, at the level of sets of variables, can be deduced from separation statements on the graph. In general the graph represents some, but not all, of the conditional independences present in the probability distribution.
The aim of this presentation is to show new minimal conditions that should be satisfied by the probability distribution in order to be able to read conditional independence statements from the covariance and from the concentration graph. We also give other conditions and other graphical statements that can be used to read now from covariance and concentration graphs conditional dependence statements between the random variables. These results are finally used to give examples of covariance and concentration which allow us to read the whole set of conditional independencies and dependencies.
Joint work with Bala Rajaratnam |
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