Statistical Learning under Nonstationary Mixing Processes
This work addresses the challenge of learning from nonstationary and dependent data, which is incremental as it combines existing relaxations of stationarity and mixing.
The authors tackled the problem of statistical learning under nonstationary mixing processes, relaxing the i.i.d. assumption by allowing both nonstationarity and mixing, and established that for bounded VC subgraph classes, the cumulative excess risk grows sublinearly in the number of predictions with a quantified rate.
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 $β$-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.