Least-square regularized regression with non-iid sampling

We study the least-square regression learning algorithm generated by regularization schemes in reproducing kernel Hilbert spaces. A non-iid setting is considered: the sequence of probability measures for sampling is not identical and the sampling may be dependent. When the sequence of marginal distr...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2009-10, Vol.139 (10), p.3579-3587
Main Authors: Pan, Zhi-Wei, Xiao, Quan-Wu
Format: Article
Language:English
Subjects:
Exact sciences and technology
General topics
Least-square regularized regression
Linear inference, regression
Markov processes
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Probability and statistics
Probability theory and stochastic processes
Reproducing kernel Hilbert space
Sampling with non-identical distributions
Sciences and techniques of general use
Statistics
Strong mixing condition
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Summary:We study the least-square regression learning algorithm generated by regularization schemes in reproducing kernel Hilbert spaces. A non-iid setting is considered: the sequence of probability measures for sampling is not identical and the sampling may be dependent. When the sequence of marginal distributions for sampling converges exponentially fast in the dual of a Hölder space and the sampling process satisfies a polynomial strong mixing condition, we derive learning rates for the learning algorithm.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2009.04.007