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Learning from dependent observations

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  • Steinwart, Ingo
  • Hush, Don
  • Scovel, Clint

Abstract

In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) only require that the data-generating process satisfies a certain law of large numbers. We then consider the learnability of SVMs for [alpha]-mixing (not necessarily stationary) processes for both classification and regression, where for the latter we explicitly allow unbounded noise.

Suggested Citation

  • Steinwart, Ingo & Hush, Don & Scovel, Clint, 2009. "Learning from dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 175-194, January.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:175-194
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    References listed on IDEAS

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    1. Irle, A., 1997. "On Consistency in Nonparametric Estimation under Mixing Conditions," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 123-147, January.
    2. Bartlett, Peter L. & Jordan, Michael I. & McAuliffe, Jon D., 2006. "Convexity, Classification, and Risk Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 138-156, March.
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    Cited by:

    1. Liu, Lu & Huang, Wei & Shen, Li, 2021. "Learning performance of regularized regression with multiscale kernels based on Markov observations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Alquier Pierre & Li Xiaoyin & Wintenberger Olivier, 2014. "Prediction of time series by statistical learning: general losses and fast rates," Dependence Modeling, De Gruyter, vol. 1, pages 65-93, January.
    3. Arrieta-Prieto, Mario & Schell, Kristen R., 2022. "Spatio-temporal probabilistic forecasting of wind power for multiple farms: A copula-based hybrid model," International Journal of Forecasting, Elsevier, vol. 38(1), pages 300-320.
    4. Katharina Strohriegl & Robert Hable, 2016. "Qualitative robustness of estimators on stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 895-917, November.
    5. Hang, H. & Steinwart, I., 2014. "Fast learning from α-mixing observations," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 184-199.
    6. Alquier Pierre & Doukhan Paul & Fan Xiequan, 2019. "Exponential inequalities for nonstationary Markov chains," Dependence Modeling, De Gruyter, vol. 7(1), pages 150-168, January.

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