A Bernstein-type inequality for some mixing processes and dynamical systems with an application to learning
部分混合过程与动力系统的Bernstein型不等式及其学习应用
We establish a Bernstein-type inequality for a class of stochastic processes that includes the classical geometrically $\phi$-mixing processes, Rio’s generalization of these processes and many time-discrete dynamical systems. Modulo a logarithmic factor and some constants, our Bernstein-type inequality coincides with the classical Bernstein inequality for i.i.d. data. We further use this new Bernstein-type inequality to derive an oracle inequality for generic regularized…