5 research outputs found
Exponential inequalities for nonstationary Markov Chains
Exponential inequalities are main tools in machine learning theory. To prove
exponential inequalities for non i.i.d random variables allows to extend many
learning techniques to these variables. Indeed, much work has been done both on
inequalities and learning theory for time series, in the past 15 years.
However, for the non independent case, almost all the results concern
stationary time series. This excludes many important applications: for example
any series with a periodic behavior is non-stationary. In this paper, we extend
the basic tools of Dedecker and Fan (2015) to nonstationary Markov chains. As
an application, we provide a Bernstein-type inequality, and we deduce risk
bounds for the prediction of periodic autoregressive processes with an unknown
period