[Forum SIS] DEC Seminar - A. Roverato - October 18th

[Raffaella Piccarreta]

AVVISO DI SEMINARIO 



DEC - Università Bocconi, 
Room 3-E4-SR03 
Via Rontgen 1 - 3rd floor 
Time: 12:30pm 



Un cordiale saluto a tutti 
Raffaella Piccarreta 

The DEC seminar schedule is available at http://www.unibocconi.eu/statseminar 

Thursday, October 18th 


Alberto Roverato 
(Università di Bologna) 

"Dichotomization invariant log-mean linear parameterization for discrete graphical models of marginal independence" 

Abstract 

Graphical models of marginal independence use a graph where every 
vertex is associated with a variable and missing edges encode marginal 
independence relationships according to a given Markov property. The 
probability distribution of a set of discrete variables is characterized by the 
associated probability table, but defining a suitable parameterization for these 
models is not straightforward. A basic requirement for the flexible implementation 
of marginal constraints is that interaction terms involving a subset of variables 
satisfy upward compatibility, that is they should reflect a property 
of the corresponding marginal distribution. Upward compatibility means 
invariance with respect to marginalization but, for discrete variables 
with arbitrary number of levels, a stronger invariance property may be 
required. Collapsing two or more levels of a discrete variables into a 
single level can be regarded as as a special kind of marginalization 
and invariance with respect to this operation is an useful feature for 
a parameterization. 

We extend the Log-Mean Linear (LML) parameterization introduced by 
Roverato, Lupparelli and La Rocca (2011, arXiv:1109.6239) for binary 
data to discrete variables with arbitrary number of levels and show 
that also in this case it can be used to parameterize graphical models 
of marginal independence. Furthermore, we show that the LML 
parameterization satisfies a stronger version of upward compatibility 
that we call dichotomization invariance. As a consequence, the LML 
parameterization allows one to simultaneously represent marginal 
independencies among variables and marginal independencies that only 
appear when certain levels are collapsed into a single one. This 
feature is useful in several applied contexts, such as genetic 
association studies. Furthermore, it provides a natural way to reduce 
the parameter count by means of substantive constraints that give 
additional insight on the dependence structure of variables. 

-- 

*************************************************** 
Raffaella Piccarreta 
DEC - Department of Decision Sciences, 
Universita' L.Bocconi, via Guglielmo Röntgen 1 (3rd floor, room D1-09). 20136, Milano. 
email: piccarreta a unibocconi.it 
tel. +39-02-58365659 / fax +39-02-58365630 

Web page (ENGLISH VERSION): http://faculty.unibocconi.eu/raffaellapiccarreta/ 
(ITALIAN VERSION): http://faculty.unibocconi.it/raffaellapiccarreta/ 
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