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

翻译：由于预测器的质量通常通过其风险来评估，因此将风险一致性视为学习方法的一个理想属性是自然的，并且许多此类方法已被证明具有风险一致性。本文的首要目标是为比以往更广泛的损失函数类建立风险一致性与 $L_p$-一致性之间的紧密联系。令人惊讶的是，将这一联系推广到偏移损失函数时，发现这种偏移在降低所需潜在概率测度的假设条件方面，并未达到与其他许多结果相同的程度。这些结果被应用于支持向量机等正则化核方法。