Generalization for slowly mixing processes

Andreas Maurer

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arXiv · 2305.00977

Generalization for slowly mixing processes

Andreas Maurer

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Abstract

A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way. For slowly mixing processes this can be a considerable advantage over results with multiplicative dependence on the mixing time. The admissible loss-classes include functions with prescribed Lipschitz norms or smoothness parameters. The bound can also be applied to be uniform over unconstrained loss-classes, where it depends on local Lipschitz properties of the function on the sample path.

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Andreas Maurer. 2023-04-28. Generalization for slowly mixing processes. https://arxiv.org/abs/2305.00977

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