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General bias/variance decomposition with target independent variance of error functions derived from the exponential family of distributions

机译：具有从指数分布族派生的误差函数的目标独立方差的一般偏差/方差分解

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摘要

An important theoretical tool in machine learning is the bias/variance decomposition of the generalization error. It was introduced for the mean square error. The bias/variance decomposition includes the concept of the average predictor. The bias is the error of the average predictor, and the systematic part of the generalization error, while the variability around the average predictor is the variance. We present a large group of error functions with the same desirable properties as the bias/variance decomposition. The error functions are derived from the exponential family of distributions via the statistical deviance measure. We prove that this family of error functions contains all error functions decomposable in that manner. We state the connection between the bias/variance decomposition and the ambiguity decomposition and present a useful approximation of ambiguity that is quadratic in the ensemble coefficients.
机译：机器学习中一个重要的理论工具是泛化误差的偏差/方差分解。它是针对均方误差引入的。偏差/方差分解包括平均预测变量的概念。偏差是平均预测变量的误差，是泛化误差的系统部分，而平均预测变量周围的变异性是方差。我们提出了一组误差函数，它们具有与偏差/方差分解相同的期望属性。误差函数是通过统计偏差度量从指数分布族导出的。我们证明该错误函数族包含所有以这种方式可分解的错误函数。我们陈述了偏差/方差分解和歧义分解之间的联系，并提出了一个有用的歧义近似值，该歧义在集合系数中是二次的。

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