主 题:Learning from dynamical system
内容简介:Statistical learning initially focuses on learning tasks such as classification, regression, on i.i.d. data. However, due to the extensive study on dynamical systems, learning tasks based on non-i.i.d. arouse wide interest. Therefore, we might assume that the non-i.i.d. data comes from one dynamical system. Specifically, we consider the C-mixing processes which are a generalization of some commonly utilized mixing processes, such as $\alpha$-mixing and $\tilde{\psi}$-mixing process. Based on this C-mixing processes, we establish a Bernstein-type inequality, which modulo a logarithmic factor and some constants, coincides with the classical one for i.i.d. processes. Utilizing this new inequality, we further derive an oracle inequality to support vector machines with Gaussian kernels for binary classification. In this manner, we obtain essentially the same rates as for i.i.d. processes. As for the least squares and quantile regression, the resulting learning rates match, up to some arbitrarily small extra term in the exponent, the optimal rates for i.i.d. processes.
报告人:杭汉源 助理教授
时 间:2018-09-06 14:30
地 点:竞慧东楼302
举办单位:统计与数学学院 澄园书院
