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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