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.
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.
Classification: 13A50, 62G07, 62H12
Keywords: Mixture model, birational, 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},
publisher = {Association des Annales de l'institut Fourier},
volume = {55},
number = {1},
year = {2005},
pages = {1-28},
doi = {10.5802/aif.2087},
zbl = {02162462},
mrnumber = {2141286},
language = {en},
url = {http://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, Volume 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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