Unsupervised performance estimation, or evaluating how well models perform on
unlabeled data is a difficult task. Recently, a method was proposed by Garg et
al. [2022] which performs much better than previous methods. Their method
relies on having a score function, satisfying certain properties, to map
probability vectors outputted by the classifier to the reals, but it is an open
problem which score function is best. We explore this problem by first showing
that their method fundamentally relies on the ordering induced by this score
function. Thus, under monotone transformations of score functions, their method
yields the same estimate. Next, we show that in the binary classification
setting, nearly all common score functions - the $L^\infty$ norm; the $L^2$
norm; negative entropy; and the $L^2$, $L^1$, and Jensen-Shannon distances to
the uniform vector - all induce the same ordering over probability vectors.
However, this does not hold for higher dimensional settings. We conduct
numerous experiments on well-known NLP data sets and rigorously explore the
performance of different score functions. We conclude that the $L^\infty$ norm
is the most appropriate.

通常用于评估模型性能的无标签数据评估的方法，通过使用得分函数映射概率向量来提高效果，但是需要选用最佳得分函数，实验得出 L^∞范数是最合适的。