Convergence and Consistency of Regularized Boosting Algorithms with Stationary B-Mixing Observations

We study the statistical convergence and consistency of regularized Boosting methods, where the samples are not independent and identically distributed(i.i.d.) but come from empirical processes of stationary β-mixing sequences. Utilizing a technique that constructs a sequence of independent blocks close in distribution to the original samples, we prove the consistency of the composite classifiers resulting from a regularization achievedby restricting the 1-norm of the base classifiers' weights. When compared to the i.i.d.