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UID:508@cran.univ-lorraine.fr
DTSTART;TZID=Europe/Paris:20240722T140000
DTEND;TZID=Europe/Paris:20240722T150000
DTSTAMP:20240719T144024Z
URL:https://www.cran.univ-lorraine.fr/events/seminaire-pardis-semnani-homa
 loidal-polynomials-and-gaussian-models-of-maximum-likelihood-degree-one/
SUMMARY:Séminaire Pardis Semnani (University of British Columbia\, Vancouv
 er)
DESCRIPTION:Speaker: Pardis Semnani (University of British Columbia\, Vanco
 uver\, Canada)\nWebsite: https://sites.google.com/view/pardissemnani/home\
 nDate: July\, 22 2024\, 14h00-15h00\nTitle: Homaloidal polynomials and Gau
 ssian models of maximum likelihood degree one\n\nAbstract:\nWe study the G
 aussian statistical models whose log-likelihood function has a unique comp
 lex critical point\, i.e.\, has maximum likelihood degree one. We exploit 
 the connection developed by Améndola et al. between the models having max
 imum likelihood degree one and homaloidal polynomials. We study the spanni
 ng tree generating function of a graph and show this polynomial is homaloi
 dal when the graph is chordal. When the graph is a cycle on n vertices\, n
 ≥4\, we prove the polynomial is not homaloidal\, and show that the maxim
 um likelihood degree of the resulting model is the nth Eulerian number. Th
 ese results support our conjecture that the spanning tree generating funct
 ion is a homaloidal polynomial if and only if the graph is chordal. We als
 o provide an algebraic formulation for the defining equations of these mod
 els. Using existing results\, we provide a computational study on construc
 ting new families of homaloidal polynomials. In the end\, we analyze the s
 ymmetric determinantal representation of such polynomials and provide an u
 pper bound on the size of the matrices involved.\n\nJoin Zoom Meeting\nhtt
 ps://cnrs.zoom.us/j/97987526601?pwd=q3O1BHYj8CBW8C9pNokhofs5baIhhD.1
CATEGORIES:Département BioSiS,Séminaires projet SiMul
LOCATION:CRAN - FST - 4ème\, Campus Sciences\, Boulevard des Aiguillettes\
 , Vandoeuvre-lès-Nancy\, 54506\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus Sciences\, Boulevard
  des Aiguillettes\, Vandoeuvre-lès-Nancy\, 54506\, France;X-APPLE-RADIUS=
 100;X-TITLE=CRAN - FST - 4ème:geo:0,0
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