Gibbs processes and applications
Information Theory has been extremely successful in utilizing probabilistic models and methods in problems like data compression, prediction, classification, and coding of information sources. Most algorithms can be classified as causal, or omni-directional: the data is processed in a directed sequential fashion: distribution of the present with respect to the past is used for prediction or classification purposes. How- ever, recently some novel approaches have been proposed in Information Theory. It turns out that the non-causal (bi-directional) approaches, i.e., when the past as well as of the future are taken into account, lead to very interesting and often superior solutions in problems like denoising (reconstruction of signals corrupted by noisy channels). The theory of Gibbs states in Statistical Mechanics - the so-called Gibbs formalism, provides a suitable framework for the description of stochastic processes in a non-causal bi-directional fashion.
With the present proposal, we aim to develop theoretical basis, as well as practical algorithms, for application of Gibbs formalism in Information Theory and Bioinformatics.