Abstract
We obtain a minimax lower bound for the expected distortion of empirically designed vector quantizers. We show that the mean squared distortion of any empirically designed vector quantizer is at least Ω (n −1/2) away from the optimal distortion for some distribution on a bounded subset of R d, where n is the number of i.i.d. data points that are used to train the empirical quantizer.
The work of the last two authors was supported by OTKA Grant F 014174.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bartlett, P., Linder, T., Lugosi, G. (1997). A minimax lower bound for empirical quantizer design. In: Ben-David, S. (eds) Computational Learning Theory. EuroCOLT 1997. Lecture Notes in Computer Science, vol 1208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62685-9_18
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DOI: https://doi.org/10.1007/3-540-62685-9_18
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