On the joint optimization of model selection and coding

The following problem is often encountered in many applications involving lossless and lossy data compression: one has m models at hand, each of which gives rise to a compression algorithm, and one wants to use these m models (or algorithms) to encode a sequence xⁿ=x₁... x_n as efficiently as possible; due to nonstationarity, the sequence xⁿ may be governed, at different time instants, by different unknown models, and the question is how to use these models to optimally encode xⁿ. In this paper, this problem is addressed by considering the joint optimization of model selection and coding, and is linked to rate distortion theory.