Fast rates in learning with dependent observations
type: Dataset
description: In this paper we tackle the problem of fast rates in time series forecasting from a statistical learning perspective. In a serie of papers (e.g. Meir 2000, Modha and Masry 1998, Alquier and Wintenberger 2012) it is shown that the main tools used in learning theory with iid observations can be extended to the prediction of time series. The main message of these papers is that, given a family of predictors, we are able to build a new predictor that predicts the series as well as the best predictor in the family, up to a remainder of order $1/\sqrt{n}$. It is known that this rate cannot be improved in general. In this paper, we show that in the particular case of the least square loss, and under a strong assumption on the time series (phi-mixing) the remainder is actually of order $1/n$. Thus, the optimal rate for iid variables, see e.g. Tsybakov 2003, and individual sequences, see \cite{lugosi} is, for the first time, achieved for uniformly mixing processes. We also show that our method is optimal for aggregating sparse linear combinations of predictors.
issued: 2026-05-27T21:39:49.294486
language: en
modified: 2026-05-27T21:39:49.294492
contact point: Organization
  fn: CCSD
keyword: fast-rates-sparsity
keyword: infoeu-reposemanticspreprint
keyword: mathmath-stmathematics-mathstatistics-mathst
keyword: mixing-processes
keyword: oracle-inequalities
keyword: pac-bayesian-bounds
keyword: preprints-working-papers-
keyword: statistical-learning-theory
keyword: statthstatistics-statstatistics-theory-statth
keyword: time-series-prediction
landing page: https://hal.science/hal-00671979

Fast rates in learning with dependent observations
type: Distribution
format: HTML
issued: 2026-05-27T21:39:49.311744
modified: 2026-05-27T21:39:49.263516
access URL: https://hal.science/hal-00671979

test_moissonnage_selune
type: Agent