no. 1
An application of classical invariant theory to identifiability in nonparametric mixtures
[Une application de la théorie classique des invariants dans les mélanges non-paramétriques]
Elmore, Ryan1 ; Hall, Peter ; Neeman, Amnon
1 Australian National University, centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, Canberra ACT 0200 (AUSTRALIE)
Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 1-28.

On sait que l'identifiabilité des mélanges multivariés se réduit à une question de géométrie algébrique. Nous résolvons cette question en étudiant des générateurs particuliers dans l'anneau des polynômes à variables vectorielles, invariants sous l'action du groupe symétrique.

It is known that the identifiability of multivariate mixtures reduces to a question in algebraic geometry. We solve the question by studying certain generators in the ring of polynomials in vector variables, invariant under the action of the symmetric group.

DOI : 10.5802/aif.2087
Classification : 13A50, 62G07, 62H12
Keywords: Mixture model, birational, invariant
Mot clés : modèle de mélange, birationel, invariant
Elmore, Ryan 1 ; Hall, Peter  ; Neeman, Amnon 

1 Australian National University, centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, Canberra ACT 0200 (AUSTRALIE) 
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Elmore, Ryan; Hall, Peter; Neeman, Amnon. An application of classical invariant theory to identifiability in nonparametric mixtures. Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 1-28. doi : 10.5802/aif.2087. http://www.numdam.org/articles/10.5802/aif.2087/

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