Anisotropic oracle inequalities in noisy quantization - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Anisotropic oracle inequalities in noisy quantization



The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X_i+\epsilon_i,i=1,\ldots,n$, where $X_i$ are i.i.d. with density $f$ and $\epsilon_i$ are i.i.d. with density $\eta$. These rates depend on the geometry of the density $f$ and the asymptotic behaviour of the characteristic function of $\eta$. This general study can be applied to the problem of $k$-means clustering with noisy data. For this purpose, we introduce a deconvolution $k$-means stochastic minimization which reaches fast rates of convergence under standard Pollard's regularity assumptions.
Fichier principal
Vignette du fichier
aoinc.pdf (253.23 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-00818307 , version 1 (26-04-2013)


  • HAL Id : hal-00818307 , version 1


Sébastien Loustau. Anisotropic oracle inequalities in noisy quantization. 2013. ⟨hal-00818307⟩
215 View
68 Download


Gmail Facebook Twitter LinkedIn More