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Joint fixedrate universal lossy coding and identification of continuousalphabet memoryless sources
 IEEE Trans. Inform. Theory
"... The problem of joint universal source coding and identification is considered in the setting of fixedrate lossy coding of continuousalphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any compactly parametrized family of R dvalued i.i.d. sources with abs ..."
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The problem of joint universal source coding and identification is considered in the setting of fixedrate lossy coding of continuousalphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any compactly parametrized family of R dvalued i.i.d. sources with absolutely continuous distributions satisfying appropriate smoothness and Vapnik–Chervonenkis learnability conditions, admits a joint scheme for universal lossy block coding and parameter estimation, such that when the block length n tends to infinity, the overhead perletter rate and the distortion redundancies converge to zero as O(n −1 log n) and O ( � n −1 log n), respectively. Moreover, the active source can be determined at the decoder up to a ball of radius O ( � n −1 log n) in variational distance, asymptotically almost surely. The system has finite memory length equal to the block length, and can be thought of as blockwise application of a timeinvariant nonlinear filter with initial conditions determined from the previous block. Comparisons are presented with several existing schemes for universal vector quantization, which do not include parameter estimation explicitly, and an extension to unbounded distortion measures is outlined. Finally, finite mixture classes and exponential families are given as explicit examples of parametric sources admitting joint universal compression and modeling schemes of the kind studied here. Keywords: Learning, minimumdistance density estimation, twostage codes, universal vector quantization, Vapnik– Chervonenkis dimension. I.
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 ..."
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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.