Consistency of Support Vector Machines for Forecasting the Evolution of an Unknown Ergodic Dynamical System from Observations with Unknown
نویسنده
چکیده
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of R and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than α-mixing.
منابع مشابه
Support Vector Machines for Forecasting the Evolution of an Unknown Ergodic Dynamical System from Observations with Unknown Noise
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, e.g., that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if a) the unknown observational noise processes is bounded and has a summable α-mixi...
متن کاملIdentification and Adaptive Position and Speed Control of Permanent Magnet DC Motor with Dead Zone Characteristics Based on Support Vector Machines
In this paper a new type of neural networks known as Least Squares Support Vector Machines which gained a huge fame during the recent years for identification of nonlinear systems has been used to identify DC motor with nonlinear dead zone characteristics. The identified system after linearization in each time span, in an online manner provide the model data for Model Predictive Controller of p...
متن کاملMachine learning algorithms in air quality modeling
Modern studies in the field of environment science and engineering show that deterministic models struggle to capture the relationship between the concentration of atmospheric pollutants and their emission sources. The recent advances in statistical modeling based on machine learning approaches have emerged as solution to tackle these issues. It is a fact that, input variable type largely affec...
متن کامل3-RPS Parallel Manipulator Dynamical Modelling and Control Based on SMC and FL Methods
In this paper, a dynamical model-based SMC (Sliding Mode Control) is proposed fortrajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring smallinertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model ofthe manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers...
متن کاملRELATIVE INFORMATION FUNCTIONAL OF RELATIVE DYNAMICAL SYSTEMS
In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007