论文标题
了解布雷格曼分歧的偏见变化权衡权衡
Understanding the bias-variance tradeoff of Bregman divergences
论文作者
论文摘要
本文基于PFAU（2013）的工作，该作品将偏差差异权衡列为任何Bregman Divergence损失函数。 PFAU（2013）表明，对于布雷格曼的差异，偏差和方差是针对中央标签定义的，该标签定义为标签变量的平均值和更复杂形式的中心预测。我们表明，与标签类似，中心预测可以解释为随机变量的平均值，其中平均值在由损耗函数本身定义的双空间中运行。通过在双空间中进行的操作查看偏见变化的权衡，我们随后得出了一些感兴趣的结果。特别是（a）差异术语满足总差异的广义定律； （b）如果无法控制随机性的来源，则其对偏差的贡献和方差具有封闭形式； （c）标签和预测空间中存在自然的结合操作，这些操作降低了方差，不会影响偏见。
This paper builds upon the work of Pfau (2013), which generalized the bias variance tradeoff to any Bregman divergence loss function. Pfau (2013) showed that for Bregman divergences, the bias and variances are defined with respect to a central label, defined as the mean of the label variable, and a central prediction, of a more complex form. We show that, similarly to the label, the central prediction can be interpreted as the mean of a random variable, where the mean operates in a dual space defined by the loss function itself. Viewing the bias-variance tradeoff through operations taken in dual space, we subsequently derive several results of interest. In particular, (a) the variance terms satisfy a generalized law of total variance; (b) if a source of randomness cannot be controlled, its contribution to the bias and variance has a closed form; (c) there exist natural ensembling operations in the label and prediction spaces which reduce the variance and do not affect the bias.
