Maximally Bijective Discretization for data-driven modeling of complex systems

Phase-space discretization is a necessary step for study of continuous dynamical systems using a language-theoretic approach. It is also critical for many machine learning techniques, e.g., probabilistic graphical models (Bayesian Networks, Markov models). This paper proposes a novel discretization method - Maximally Bijective Discretization, that finds a discretization on the dependent variables given a discretization on the independent variables such that the correspondence between input and output variables in the continuous domain is preserved in discrete domain for the given dynamical system.