Noise Separation and MDL Modeling of Chaotic Processes

The noise separation problem is one in which observed data are expressed as the sum of two parts, a ‘smooth’ signal generated by a chaotic dynamical system, and the ‘noise’. The optimally smooth signal is defined as that chaotic process which permits encoding of the observed data, including the signal generating dynamical system and the noise distribution, with the fewest number of bits. A numerical solution is described, where successive approximations are computed with a powerful algorithm Context, capable of recovering any Markov process from the data it generates.