  The problem of joint universal source coding and modeling, treated in the
context of lossless codes by Rissanen, was recently generalized to fixed-rate
lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We
extend these results to variable-rate lossy block coding of stationary ergodic
sources and show that, for bounded metric distortion measures, any finitely
parametrized family of stationary sources satisfying suitable mixing,
smoothness and Vapnik-Chervonenkis learnability conditions admits universal
schemes for joint lossy source coding and identification. We also give several
explicit examples of parametric sources satisfying the regularity conditions.
