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Anisotropic oracle inequalities in noisy quantization

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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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Dates and versions

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

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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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