Threshold methods are popular for ordinal regression problems, which are
classification problems for data with a natural ordinal relation. They learn a
one-dimensional transformation (1DT) of observations of the explanatory
variable, and then assign label predictions to the observations by thresholding
their 1DT values. In this paper, we study the influence of the underlying data
distribution and of the learning procedure of the 1DT on the classification
performance of the threshold method via theoretical considerations and
numerical experiments. Consequently, for example, we found that threshold
methods based on typical learning procedures may perform poorly when the
probability distribution of the target variable conditioned on an observation
of the explanatory variable tends to be non-unimodal. Another instance of our
findings is that learned 1DT values are concentrated at a few points under the
learning procedure based on a piecewise-linear loss function, which can make
difficult to classify data well.

通过理论考虑和数值实验，本文研究了阈值法在阶序回归问题中的分类性能与数据分布以及一维转换学习程序之间的影响。研究发现，当目标变量在解释变量条件下的概率分布趋向于非单峰分布时，基于典型学习程序的阈值法可能表现不佳。此外，基于分段线性损失函数的学习程序得到的一维转换值集中于少数几个点，这可能导致难以对数据进行良好的分类。