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Anisotropic oracle inequalities in noisy quantization

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00818307
Contributor : Sébastien Loustau <>
Submitted on : Friday, April 26, 2013 - 3:26:34 PM
Last modification on : Monday, March 9, 2020 - 6:16:02 PM
Document(s) archivé(s) le : Saturday, July 27, 2013 - 4:20:08 AM

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  • HAL Id : hal-00818307, version 1

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Sébastien Loustau. Anisotropic oracle inequalities in noisy quantization. 2013. ⟨hal-00818307⟩

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