Risk-sensitive loss in kernel space for robust adaptive filtering

Recently, a robust cost function called C-Loss was proposed for signal processing and machine learning, which is essentially the mean square error (MSE) in a reproducing kernel Hilbert space (RKHS). In this paper, we propose a new cost function, called the kernelized risk-sensitive (KRS), which is, in essence, the risk-sensitive loss in kernel space. The risk-sensitive cost is a well-known optimization cost in control and estimation communities. In estimation theory, the risk-sensitive cost is defined as the expectation of an exponential function of the squared estimation error. The KRS cost is insensitive to large outliers and can be applied in robust adaptive filtering. Compared with C-Loss, the KRS can achieve faster convergence speed especially when filter is far away from the optimal solution.