Abstract
We study a special case of the problem of statistical learning without the
i.i.d. assumption. Specifically, we suppose a learning method is presented with
a sequence of data points, and required to make a prediction (e.g., a
classification) for each one, and can then observe the loss incurred by this
prediction. We go beyond traditional analyses, which have focused on stationary
mixing processes or nonstationary product processes, by combining these two
relaxations to allow nonstationary mixing processes. We are particularly
interested in the case of $\beta$-mixing processes, with the sum of changes in
marginal distributions growing sublinearly in the number of samples. Under
these conditions, we propose a learning method, and establish that for bounded
VC subgraph classes, the cumulative excess risk grows sublinearly in the number
of predictions, at a quantified rate.
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