This paper investigates an interesting weakly supervised regression setting
called regression with interval targets (RIT). Although some of the previous
methods on relevant regression settings can be adapted to RIT, they are not
statistically consistent, and thus their empirical performance is not
guaranteed. In this paper, we provide a thorough study on RIT. First, we
proposed a novel statistical model to describe the data generation process for
RIT and demonstrate its validity. Second, we analyze a simple selection method
for RIT, which selects a particular value in the interval as the target value
to train the model. Third, we propose a statistically consistent limiting
method for RIT to train the model by limiting the predictions to the interval.
We further derive an estimation error bound for our limiting method. Finally,
extensive experiments on various datasets demonstrate the effectiveness of our
proposed method.

本文研究了一种弱监督回归设置，称为区间目标回归 (RIT)，提出了一种新的统计模型，分析了一种简单的选择方法和一种统计一致的限制方法，并进一步推导了该方法的估计误差界限。针对不同数据集的实验结果证明了该方法的有效性。