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Joint universal lossy coding and identification of stationary mixing sources with general alphabets
 IEEE Trans. Inform. Theory
"... We consider the problem of joint universal variablerate lossy coding and identification for parametric classes of stationary βmixing sources with general (Polish) alphabets. Compression performance is measured in terms of Lagrangians, while identification performance is measured by the variational ..."
Abstract

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We consider the problem of joint universal variablerate lossy coding and identification for parametric classes of stationary βmixing sources with general (Polish) alphabets. Compression performance is measured in terms of Lagrangians, while identification performance is measured by the variational distance between the true source and the estimated source. Provided that the sources are mixing at a sufficiently fast rate and satisfy certain smoothness and Vapnik–Chervonenkis learnability conditions, it is shown that, for bounded metric distortions, there exist universal schemes for joint lossy compression and identification whose Lagrangian redundancies converge to zero as � Vn log n/n as the block length n tends to infinity, where Vn is the Vapnik–Chervonenkis dimension of a certain class of decision regions defined by the ndimensional marginal distributions of the sources; furthermore, for each n, the decoder can identify ndimensional marginal the active source up to a ball of radius O ( � Vn log n/n) in variational distance, eventually with probability one. The results are supplemented by several examples of parametric sources satisfying the regularity conditions. Keywords: Learning, minimumdistance density estimation, twostage codes, universal vector quantization, Vapnik– Chervonenkis dimension. I.