A New L₁ Multi-Kernel Learning Support Vector Regression Ensemble Algorithm With AdaBoost

This paper proposes a new multi-kernel learning ensemble algorithm, called Ada-
$L_{1}$
MKL-WSVR, which can be regarded as an extension of multi-kernel learning (MKL) and weighted support vector regression (WSVR). The first novelty is to add the
$L_{1}$
norm of the weights of the combined kernel function to the objective function of WSVR, which is used to adaptively select the optimal base models and their parameters. In addition, an accelerated method based on fast iterative shrinkage thresholding algorithm (FISTA) is developed to solve the weights of the combined kernel function. The second novelty is to propose an integrated learning framework based on AdaBoost, named Ada-
$L_{1}$
MKL-WSVR. In this framework, we integrate FISTA into AdaBoost. At each iteration, we optimize the weights of the combined kernel function and update the weights of the training samples at the same time. Then an ensemble regression function of a set of regression functions is output. Finally, two groups of the experiments are designed to verify the performance of our algorithm. On the first group of the experiments including eight datasets from UCI machine learning repository, the MAEs and RMSEs of Ada-
$L_{1}$
MKL-WSVR are reduced by 11.14% and 9.08% on average, respectively. Furthermore, on the second group of the experiments including the COVID-19 epidemic datasets from eight countries, the MAEs and RMSEs of Ada-
$L_{1}$
MKL-WSVR are reduced by 31.19% and 29.98% on average, respectively.