Fast rates for empirical vector quantization

Clément Levrard (1, 2)

1 SELECT - Model selection in statistical learning
2 Laboratoire de probabilités et statistiques d'Orsay

We consider the rate of convergence of the expected loss of empirically optimal vector quantizers. Earlier results show that the mean-squared expected distortion for any fixed distribution supported on a bounded set and satisfying some regularity conditions decreases at the rate O(log n/n). We prove that this rate is actually O(1/n). Although these conditions are hard to check, we show that well-polarized distributions with continuous densities supported on a bounded set are included in the scope of this result.

Mots clés: quantization; classification; localization principle

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Clément Levrard. Fast rates for empirical vector quantization. 2011. ⟨hal-00664068⟩