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Fast learning from α-mixing observations

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  • Hang, H.
  • Steinwart, I.

Abstract

We present a new oracle inequality for generic regularized empirical risk minimization algorithms learning from stationary α-mixing processes. Our main tool to derive this inequality is a rather involved version of the so-called peeling method. We then use this oracle inequality to derive learning rates for some learning methods such as empirical risk minimization (ERM), least squares support vector machines (SVMs) using given generic kernels, and SVMs using the Gaussian RBF kernels for both least squares and quantile regression. It turns out that for i.i.d. processes our learning rates for ERM and SVMs with Gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates, while in the remaining cases our rates are at least close to the optimal rates.

Suggested Citation

  • Hang, H. & Steinwart, I., 2014. "Fast learning from α-mixing observations," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 184-199.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:184-199
    DOI: 10.1016/j.jmva.2014.02.012
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    References listed on IDEAS

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    1. Steinwart, Ingo & Hush, Don & Scovel, Clint, 2009. "Learning from dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 175-194, January.
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    Cited by:

    1. Fan, Xiequan & Alquier, Pierre & Doukhan, Paul, 2022. "Deviation inequalities for stochastic approximation by averaging," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 452-485.
    2. 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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