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Abstract:
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Learning algorithms are almost always investigated under the assumption of random samples, where in most cases, the randomness is in form of an i.i.d. process. In this talk I will present some recent results describing when learning is also possible from ergodic dynamical systems, that is, from essentially deterministic time series. Besides some more general consistency results I will mainly focus on certain classes of dynamical systems for which we have a fast decay of correlations for restricted classes of functions. To this end, I will first present a Bernstein-type concentration inequality for such systems. In a second step I will then illustrate the use of this inequality for classification and regression learning from dynamical systems, density estimation, and system forecasting.
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