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.
Keywords: Mixture model, birational, invariant
Mot 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{\textquoteright}institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2087}, mrnumber = {2141286}, zbl = {02162462}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2087/} }
TY - JOUR AU - Elmore, Ryan AU - Hall, Peter AU - Neeman, Amnon TI - An application of classical invariant theory to identifiability in nonparametric mixtures JO - Annales de l'Institut Fourier PY - 2005 SP - 1 EP - 28 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2087/ DO - 10.5802/aif.2087 LA - en ID - AIF_2005__55_1_1_0 ER -
%0 Journal Article %A Elmore, Ryan %A Hall, Peter %A Neeman, Amnon %T An application of classical invariant theory to identifiability in nonparametric mixtures %J Annales de l'Institut Fourier %D 2005 %P 1-28 %V 55 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2087/ %R 10.5802/aif.2087 %G en %F 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/articles/10.5802/aif.2087/
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