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Section: New Results

Intermediate dependency generative models

Participants : Christophe Biernacki, Matthieu Marbac-Lourdelle, Vincent Vandewalle.

Defining generative models for dealing with possibly correlated categorical variables is at the core of the modal activity. We start by noticing that it is straightforward to build a full independent distribution $\mathring{p}$ and also a full dependent one $\acute{p}$ in the categorical situation. However, both are usually too crude for modelizing most of real situations.

Our idea is to combine both extreme distributions $\mathring{p}$ and $\acute{p}$ in order to obtain a new distribution called $\tilde{p}$ (i) which is an intermediate dependent situation between full independence and full dependence and (ii) which is not degenerate. As a consequence, $\tilde{p}$ is a meaningful distribution because its particular “positioning” between $\mathring{p}$ and $\acute{p}$ directly models and reveals strength of dependency between variables.

In addition, since both $\mathring{p}$ and $\acute{p}$ are easily available for most variables types, we expect to be able to design a distribution $\tilde{p}$ for most variables types, and not also the categorical ones.

A PhD thesis started on October'11 on this topic in continuation of the Master's thesis of Matthieu Marbac-Lourdelle [37] .