2018/10/03 by Orlando Romero, Romero, Orlando, Sarthak Chatterjee +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1810.02022
openalex publication_date 2018/10/03 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
In this paper, we propose a dynamical systems perspective of the\nExpectation-Maximization (EM) algorithm. More precisely, we can analyze the EM\nalgorithm as a nonlinear state-space dynamical system. The EM algorithm is\nwidely adopted for data clustering and density estimation in statistics,\ncontrol systems, and machine learning. This algorithm belongs to a large class\nof iterative algorithms known as proximal point methods. In particular, we\nre-interpret limit points of the EM algorithm and other local maximizers of the\nlikelihood function it seeks to optimize as equilibria in its dynamical system\nrepresentation. Furthermore, we propose to assess its convergence as asymptotic\nstability in the sense of Lyapunov. As a consequence, we proceed by leveraging\nrecent results regarding discrete-time Lyapunov stability theory in order to\nestablish asymptotic stability (and thus, convergence) in the dynamical system\nrepresentation of the EM algorithm.\n