Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
This work provides theoretical guarantees for statistical learning methods under weak dependence assumptions, which is incremental but important for handling non-i.i.d. data in machine learning.
The authors derived a Bernstein-type inequality for sums of weakly dependent Banach-valued random variables and applied it to analyze error upper bounds for spectral regularization methods in reproducing kernel decision rules, showing asymptotic results for samples from τ-mixing processes.
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a $τ-$mixing process.