Exponential inequalities for nonstationary Markov Chains

08/27/2018
by   Pierre Alquier, et al.
0

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 behaviour 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/10/2023

Rosenthal-type inequalities for linear statistics of Markov chains

In this paper, we establish novel deviation bounds for additive function...
research
06/06/2018

Rademacher complexity for Markov chains : Applications to kernel smoothing and Metropolis-Hasting

Following the seminal approach by Talagrand, the concept of Rademacher c...
research
12/30/2019

Iterated Jackknives and Two-Sided Variance Inequalities

We consider the variance of a function of n independent random variables...
research
06/30/2020

Exponential inequalities for sampling designs

In this work we introduce a general approach, based on the mar-tingale r...
research
04/12/2022

Hold-out estimates of prediction models for Markov processes

We consider the selection of prediction models for Markovian time series...
research
07/03/2019

Deviation inequalities for separately Lipschitz functionals of composition of random functions

We consider a class of non-homogeneous Markov chains, that contains many...
research
08/22/2023

Identification and validation of periodic autoregressive model with additive noise: finite-variance case

In this paper, we address the problem of modeling data with periodic aut...

Please sign up or login with your details

Forgot password? Click here to reset