# Statistical Learning under Nonstationary Mixing Processes

arXiv: https://arxiv.org/abs/1512.08064 · HTML: https://mlsanity.com/paper/1512.08064/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2015.

## Built on by (most cited first, 12 of 12)

- [An Adaptive Algorithm for Learning with Unknown Distribution Drift](https://mlsanity.com/paper/2305.02252/) (2023)
- [Nonparametric Density Estimation under Distribution Drift](https://mlsanity.com/paper/2302.02460/) (2023)
- [Adaptive Smooth Non-Stationary Bandits](https://mlsanity.com/paper/2407.08654/) (2024)
- [An Improved Algorithm for Learning Drifting Discrete Distributions](https://mlsanity.com/paper/2403.05446/) (2024)
- [Adaptive Estimation and Learning under Temporal Distribution Shift](https://mlsanity.com/paper/2505.15803/) (2025)
- [Optimal Empirical Risk Minimization under Temporal Distribution Shifts](https://mlsanity.com/paper/2507.13287/) (2025)
- [An Adaptive Method for Weak Supervision with Drifting Data](https://mlsanity.com/paper/2306.01658/) (2023)
- [Fast Rates for Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2602.05742/) (2026)
- [On the Change of Decision Boundaries and Loss in Learning with Concept Drift](https://mlsanity.com/paper/2212.01223/) (2022)
- [A Remark on Concept Drift for Dependent Data](https://mlsanity.com/paper/2312.10212/) (2023)
- [Efficiently Learning Drifting Halfspaces with Massart Noise](https://mlsanity.com/paper/2606.11149/) (2026)
- [Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2610.13598/) (2026)

## Abstract (arXiv)

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.