Discrepancy-Based Theory and Algorithms for Forecasting Non-Stationary Time Series

Vitaly Kuznetsov; Mehryar Mohri

doi:10.1007/s10472-019-09683-1

Discrepancy-Based Theory and Algorithms for Forecasting Non-Stationary Time Series

Vitaly Kuznetsov, Mehryar Mohri

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. Our learning bounds guide the design of new algorithms for non-stationary time series forecasting for which we report several favorable experimental results.

Original language	English (US)
Pages (from-to)	367-399
Number of pages	33
Journal	Annals of Mathematics and Artificial Intelligence
Volume	88
Issue number	4
DOIs	https://doi.org/10.1007/s10472-019-09683-1
State	Published - Apr 1 2020

Keywords

Discrepancy
Expected sequential covering numbers
Forecasting
Generalization bounds
Non-mixing
Non-stationary
Sequential Rademacher complexity
Time series

ASJC Scopus subject areas

Artificial Intelligence
Applied Mathematics

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title = "Discrepancy-Based Theory and Algorithms for Forecasting Non-Stationary Time Series",

abstract = "We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. Our learning bounds guide the design of new algorithms for non-stationary time series forecasting for which we report several favorable experimental results.",

keywords = "Discrepancy, Expected sequential covering numbers, Forecasting, Generalization bounds, Non-mixing, Non-stationary, Sequential Rademacher complexity, Time series",

author = "Vitaly Kuznetsov and Mehryar Mohri",

note = "Funding Information: This work was partly funded by NSF CCF-1535987, IIS-1618662, and a Google Research Award. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

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AU - Mohri, Mehryar

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N2 - We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. Our learning bounds guide the design of new algorithms for non-stationary time series forecasting for which we report several favorable experimental results.

AB - We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. Our learning bounds guide the design of new algorithms for non-stationary time series forecasting for which we report several favorable experimental results.

KW - Discrepancy

KW - Expected sequential covering numbers

KW - Forecasting

KW - Generalization bounds

KW - Non-mixing

KW - Non-stationary

KW - Sequential Rademacher complexity

KW - Time series

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Discrepancy-Based Theory and Algorithms for Forecasting Non-Stationary Time Series

Abstract

Keywords

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