The Living Thing / Notebooks : Statistical learning theory for dependent data

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