Modeling with renormalization group and randomization.

Abstract

With the development of science and technology, modeling methods have been applied in many fields such as science, industry, medicine, biology and finance. This thesis develops some new techniques helping to get good and reliable models in statistical learning, system identification, optimization and control. The thesis first proposes a new method for model assessment based on Renormalization Group. Then, the thesis proposes an improved system identification method with Renormalization Group. Next, a fast algorithm is proposed for formally solving the outlier detection problem for dynamic systems. A novel approach based on under-sampling with averaging is developed to deal with large noise. In addition, the thesis proposes a brand-new method for global optimization by randomized group search in contracting regions. Moreover, the thesis proposes a method for determining the stabilizing parameter regions for general delay control systems based on randomized sampling.