Self-normalized Bernstein Inequalities for Regenerative Processes and Applications to Learning Without Independence

Imon Banerjee, Pierre Alquier|October 21, 2026arXiv

Key Takeaway

You can train classifiers on dependent, non-i.i.d. data and still get theoretical guarantees on generalization error if the data has a regenerative structure (cycles), making learning theory applicable to realistic scenarios like time series.

Summary

This paper develops statistical inequalities for learning from non-independent data that follows a regenerative process (data organized into cycles).

training evaluation data

Key Terms

regenerative-process self-normalized-bernstein-inequality non-iid-data oracle-inequality minimax-optimal