Robust learning of maximum correntropy criterion with α-mixing sequence

As a robust learning criterion, the maximum correntropy criterion (MCC) is effective for regression tasks contaminated by outliers and heavy-tailed noise, and serves as a favorable alternative to the least square method in non-Gaussian noise environments. However, almost all existing theoretical studies on MCC are established under the independent and identically distributed (i.i.d.) data assumption, which does not accord with the prevalent dependence features of real-world data. To tackle this issue, this paper investigates MCC-based robust empirical risk minimization (ERM) scheme over non-i.i.d. α-mixing dependent sequences. Using the Bernstein inequality for exponentially strongly mixing sequences, we analyze the generalization and prediction performance of the MCC estimator and establish its fast convergence rates under the α-mixing framework. Numerical simulations demonstrate that MCC retains superior robustness against heavy-tailed noise on dependent data with α-mixing structures.