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.
Classification : 13A50, 62G07, 62H12
Mots clés : modèle de mélange, birationel, invariant
@article{AIF_2005__55_1_1_0, author = {Elmore, Ryan and Hall, Peter and Neeman, Amnon}, title = {An application of classical invariant theory to identifiability in nonparametric mixtures}, journal = {Annales de l'Institut Fourier}, pages = {1--28}, publisher = {Association des Annales de l'institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2087}, zbl = {02162462}, mrnumber = {2141286}, language = {en}, url = {www.numdam.org/item/AIF_2005__55_1_1_0/} }
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/item/AIF_2005__55_1_1_0/
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