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© INRIA Sophie Auvin - P comme Protocole

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Géométrie algébrique convexe

4/07/2013

This lecture concerns convex bodies with an interesting algebraic structure. Our primary focus is on the geometry of semidefinite optimization. Starting with elementary questions about ellipses in the plane, we move on to discuss the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.

Lieu : Université Pierre et Marie Curie, 4 place Jussieu, tour Zamansky (tour centrale, salle 24-00)

Intervenant(s) : Bernd Sturmfels

Mots-clés :

Accueil > Centre > Paris > Agenda > Géométrie algébrique convexe

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© INRIA Sophie Auvin - P comme Protocole

Séminaire des équipes de recherche

Maximum Likelihood for Matrices with Rank Constraints

5/07/2013

Maximum likelihood estimation is a fundamental computational task in statistics. We discuss this problem for manifolds of low rank matrices. These represent mixtures of independent distributions of two discrete random variables. This non-convex optimization problems leads to some beautiful geometry, topology, and combinatorics. We explain how numerical algebraic geometry is used to find the global maximum of the likelihood function, and we present a remarkable duality theorem due to Draisma and Rodriguez.

Lieu : Université Pierre et Marie Curie, 4 place Jussieu, salle 25-26/101 (Laurière)

Intervenant(s) : Bernd Sturmfels

Mots-clés :

Accueil > Centre > Paris > Agenda > Maximum Likelihood for Matrices with Rank Constraints

lire la suite

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