Anisotropic oracle inequalities in noisy quantization
| Autor: | Loustau, S��bastien |
|---|---|
| Přispěvatelé: | Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Loustau, Sébastien |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Statistics::Theory margin assumption [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH] Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] deconvolution k-means clustering fast rates Statistics - Machine Learning [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Quantization FOS: Mathematics [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] |
| Popis: | 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. Comment: 30 pages. arXiv admin note: text overlap with arXiv:1205.1417 |
| Databáze: | OpenAIRE |
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