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As a predictor's quality is often assessed by means of its risk, it isnatural to regard risk consistency as a desirable property of learning methods,and many such methods have indeed been shown to be risk consistent. The firstaim of this paper is to establish the close connection between risk consistencyand $L_p$-consistency for a considerably wider class of loss functions than hasbeen done before. The attempt to transfer this connection to shifted lossfunctions surprisingly reveals that this shift does not reduce the assumptionsneeded on the underlying probability measure to the same extent as it does formany other results. The results are applied to regularized kernel methods suchas support vector machines.

On the Connection between $L_p$ and Risk Consistency and its Implications on Regularized Kernel Methods