Robust low-rank multiple kernel learning with compound regularization

Kernel learning is widely used in nonlinear models during the implementation of forecasting tasks in analytics. However, existing forecasting models lack robustness and accuracy. Therefore, in this study, a novel supervised forecasting approach based on robust low-rank multiple kernel learning with compound regularization is investigated. The proposed method extracts the benefits from robust regression, multiple kernel learning with low-rank approximation, and sparse learning systems. Unlike existing hybrid forecasting methods, which frequently combine different models in parallel, we embed a Huber or quantile loss function and a compound regularization composed of smoothly clipped absolute deviation and ridge regularizations in a support vector machine with predefined number of kernels. To select the optimal kernels, L1 penalization with positive constraint is also considered. The proposed model exhibits robustness, forecasting accuracy, and sparsity in the reproducing kernel Hilbert space. For computation, a simple algorithm is designed based on local quadratic approximation to implement the proposed method. Theoretically, the forecasting and estimation error bounds of the proposed estimators are derived under a null consistency assumption. Real data experiments using datasets from various scientific research fields demonstrate the superior performances of the proposed approach compared with other state-of-the-art competitors.