Linear regression

Gene

Quantum mechanics

Algorithm

Chaotic

Statistics

Applied mathematics

Robustness (evolution)

Lorenz system

Biochemistry

Computer science

Statistical physics

Regression analysis

Outlier

Physics

Nonlinear system

Nonlinear regression

Regression

Mathematics

Robust regression

Artificial intelligence

Chemistry

Machine learning

Chaos An Interdisciplinary Journal of Nonlinear Science

In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows robustness toward noise and outliers and it outperforms many of the current state-of-the-art methods. Moreover, the method of Entropic Regression overcomes many of the major limitations of the current methods such as sloppy parameters, diverse scale, and SID in high dimensional systems such as complex networks. The use of information-theoretic measures in entropic regression poses unique advantages, due to the Asymptotic Equipartition Property (AEP) of probability distributions, that outliers and other low-occurrence events are conveniently and intrinsically de-emphasized as not-typical, by definition. We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double Well Potential.

How entropic regression beats the outliers problem in nonlinear system identification