Statistical learning theory for dependent data such as time series and other dpendency structures.

Non-stationary, non-asymptotic bounds please. Keywords: Ergodic, α-, β-mixing.

Mohri and Kuznetsov have done lots of work here; See, e.g. their NIPS2016 tutorial, or KuMo16.

## Refs

- AlLW13
- Alquier, P., Li, X., & Wintenberger, O. (2013) Prediction of time series by statistical learning: general losses and fast rates.
*Dependence Modeling*, 1, 65–93. DOI. - AlWi12
- Alquier, P., & Wintenberger, O. (2012) Model selection for weakly dependent time series forecasting.
*Bernoulli*. - CKMY16
- Cortes, C., Kuznetsov, V., Mohri, M., & Yang, S. (2016) Structured Prediction Theory Based on Factor Graph Complexity. In D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, & R. Garnett (Eds.), Advances in Neural Information Processing Systems 29 (pp. 2514–2522). Curran Associates, Inc.
- KoCM08
- Kontorovich, L. (Aryeh), Cortes, C., & Mohri, M. (2008) Kernel methods for learning languages.
*Theoretical Computer Science*, 405(3), 223–236. DOI. - KoCM06
- Kontorovich, L., Cortes, C., & Mohri, M. (2006) Learning Linearly Separable Languages. In J. L. Balcázar, P. M. Long, & F. Stephan (Eds.), Algorithmic Learning Theory (pp. 288–303). Springer Berlin Heidelberg
- KuMo14
- Kuznetsov, V., & Mohri, M. (2014) Forecasting Non-Stationary Time Series: From Theory to Algorithms.
- KuMo15
- Kuznetsov, V., & Mohri, M. (2015) Learning Theory and Algorithms for Forecasting Non-Stationary Time Series. In Advances in Neural Information Processing Systems (pp. 541–549). Curran Associates, Inc.
- KuMo16
- Kuznetsov, V., & Mohri, M. (2016) Generalization Bounds for Non-stationary Mixing Processes. In Machine Learning Journal.
- McSS11a
- McDonald, D. J., Shalizi, C. R., & Schervish, M. (2011a) Generalization error bounds for stationary autoregressive models.
*arXiv:1103.0942 [Cs, Stat]*. - McSS11b
- McDonald, D. J., Shalizi, C. R., & Schervish, M. (2011b) Risk bounds for time series without strong mixing.
*arXiv:1106.0730 [Cs, Stat]*. - MoRo09
- Mohri, M., & Rostamizadeh, A. (2009) Rademacher complexity bounds for non-iid processes. In Advances in Neural Information Processing Systems (pp. 1097–1104).
- RaST14
- Rakhlin, A., Sridharan, K., & Tewari, A. (2014) Sequential complexities and uniform martingale laws of large numbers.
*Probability Theory and Related Fields*, 161(1–2), 111–153. DOI. - Geer02
- van de Geer, S. (2002) On Hoeffdoing’s inequality for dependent random variables. In Empirical Process Techniques for Dependent Data. Birkhhäuser