Rigorous Theory for General Non‑IID Learning Beyond the Structured Setting

Establish a rigorous theoretical characterization of learning with general non‑i.i.d. data beyond the causal structured k‑gap independent setting analyzed in this work, including precise generalization guarantees for kernel ridge regression.

Background

The authors develop concentration tools and excess risk bounds for KRR under a specific structured non‑i.i.d. model with causal signal–noise structure and k‑gap independence, showing how dependencies and noise multiplicity affect generalization.

They explicitly acknowledge a limitation: their analysis is confined to this structured regime, and they identify the broader task of rigorously characterizing general non‑i.i.d. scenarios as an open problem.

References

Our limitations are twofold: (i) we only establish the learnability of individual score function but no fully characterization of the sampling error throughout the entire denoising process, and (ii) our analysis is confined to structured non-i.i.d. settings, leaving a rigorous theoretical characterization of general non-i.i.d. scenarios as an open problem.

— Kernel Regression in Structured Non-IID Settings: Theory and Implications for Denoising Score Learning  (2510.15363 - Zhang et al., 17 Oct 2025) in Conclusion and Limitations

An extension to unbounded, for example sub-Gaussian or sub-exponential, innovations would require uniform conditional Bernstein-type moment bounds for $Z_t := \bigl(X_{t+1}-f_\star(X_t)\bigr)\phi_\lambda(X_t)$, together with a corresponding concentration inequality for Hilbert-valued martingales. We leave this extension for future work.

— Markov Chain Convergence in Kernel-Induced Geometry  (2610.13916 - Kachaiev et al., 9 Oct 2026) in Section 3, paragraph “Bounded domain”

Appendix~\ref{app:rademacher} provides a uniform extension over hypothesis classes using Block Rademacher Complexity, while a fuller treatment of model selection and training under dependence remains open.

— Reliable Risk Estimation with Kernel Mean Matching under Dependent Sampling  (2610.18292 - Zaytsev et al., 13 Oct 2026) in Section 5, Conclusion and Limitations, paragraph “Limitations and Future Work”