A note on the numerical solutions of kernel-based learning problems

M. Scandella, M. Mazzoleni, S. Formentin, F. Previdi

In the last decade, kernel-based learning approaches typically employed for classification and regression have shown outstanding performance also in dynamic system identification. For this reason, they are now widely recognized as convenient tools to solve complex model-based control design problems. A key assumption in such learning techniques is that the kernel matrix is non-singular. However, due to limited machine precision, this might not be the case in many practical applications. In this work, we analyze the above problem and show that such an apparent disadvantage actually introduces additional freedom, e.g., to enforce sparsity or to accurately solve ill-conditioned problems such as semi-supervised regression.