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The minimax distortion redundancy in empirical quantizer design
Bartlett, Peter; Linder, Tamas; Lugosi, Gábor
Universitat Pompeu Fabra. Departament d'Economia i Empresa
We obtain minimax lower and upper bounds for the expected distortionredundancy of empirically designed vector quantizers. We show that the meansquared distortion of a vector quantizer designed from $n$ i.i.d. datapoints using any design algorithm is at least $\Omega (n^{-1/2})$ awayfrom the optimal distortion for some distribution on a bounded subset of${\cal R}^d$. Together with existing upper bounds this result shows thatthe minimax distortion redundancy for empirical quantizer design, as afunction of the size of the training data, is asymptotically on the orderof $n^{1/2}$. We also derive a new upper bound for the performance of theempirically optimal quantizer.
Statistics, Econometrics and Quantitative Methods
hypothesis testing
statistical decision theory: operations research
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