AI 中文总结
本研究针对有序回归，提出一种规避尺度相关偏差的新型促进单峰性的正则化学习（UPRL）方法，经实验验证其可提升预测性能，尤其适配小或大规模训练数据场景。
AI 中文摘要
有序回归，又称有序分类，是对有序数据的分类，其中潜在目标变量为类别型且具有自然的有序关系。过往研究表明，在许多真实有序数据中，给定解释变量取值时目标变量的条件概率分布（CPD）在解释变量的大部分定义域内呈单峰形态，即使在剩余定义域内也接近单峰。因此，促进单峰性的正则化学习（UPRL）可推动预测的CPD更接近单峰，以降低预测方差且不会给具有单峰性的有序数据引入过多偏差，有望提升预测性能，尤其在小尺寸训练数据场景下。本研究指出，过往UPRL方法不仅会推动预测的CPD更接近单峰，还会使其尺度更大（即更平滑或置信度更低）。据此，我们开发了一种更严格体现UPRL理念且规避尺度相关偏差的新方法，通过实验对比验证了促进单峰性确实有助于提升预测性能。此外，与过往UPRL方法相比，所提UPRL方法在更小规模数据或更大规模训练数据场景下表现更优，我们的分析从是否存在意外尺度相关偏差的角度解释了这一实验观察结果。
英文摘要
Ordinal regression, also called ordinal classification, is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation. Previous works have indicated that, in many real-world ordinal data, the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable would be unimodal in a large domain of the explanatory variable and close to be unimodal even in a remaining domain. Therefore, unimodality-promoting regularized learning (UPRL), which promotes a predicted CPD closer to be unimodal with the aim of decreasing a prediction variance without inducing much bias for ordinal data of the unimodality, is promising to improve the prediction performance especially with small-size training data. In this study, we show that previous UPRL methods promote a predicted CPD to not only become closer to be unimodal but also have a larger scale (in other words, be smoother or less-confident). Therefore, we develop a novel method that more strictly reflects the idea of UPRL and evades a scale-related bias, and verify through experimental comparison that the unimodality-promotion indeed contributes to improve the prediction performance. Additionally, while our proposed UPRL method could perform better for smaller-scale data or with larger-size training data compared to a previous UPRL method, our analysis explains this experimental observation in terms of the presence or absence of an unexpected scale-related bias.
