2017/08/17 by Sean Alan Ali, Carlo Cafaro
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Artificial intelligence #Complex Systems and Time Series Analysis #Computer science #Data mining #Dynamical systems theory #Focus (optics) #Identification (biology) #Inference #Information theory #Mathematics #Measure (data warehouse) #Neural Networks and Applications #Physical system #Physics #Probabilistic logic #Statistical Mechanics and Entropy #Statistical model #Theoretical computer science #math-ph #math.MP
paper · pdf · doi:10.1142/s0129055x17300023
published as Rev. Math. Phys. 29, 1730002 (2017) · 47 pages
openalex publication_date 2017/08/17 · openalex created_date 2017/08/31 · arxiv created 2017/09/07 · arxiv updated 2017/10/11 · openalex updated_date 2026/08/05
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. The existence of fundamental links among physical systems, dynamical equations, experimental data and statistical modeling motivate us to present in this paper our theoretical modeling scheme which combines information geometry and inductive inference methods to provide a probabilistic description of complex systems in the presence of limited information. Special focus is devoted to describe the role of our entropic information geometric complexity measure. In particular, we provide several illustrative examples wherein our modeling scheme is used to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, limitations, possible improvements, and future investigations are discussed.