Title: Approximately Unimodal Likelihood Models for Ordinal Regression Show Chinese title

Title: 近似单峰似然模型用于有序回归

Abstract: Ordinal regression (OR, 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 for the underlying explanatory variable. A key to successful OR models is to find a data structure `natural ordinal relation' common to many ordinal data and reflect that structure into the design of those models. A recent OR study found that many real-world ordinal data show a tendency that the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable will often be unimodal. Several previous studies thus developed unimodal likelihood models, in which a predicted CPD is guaranteed to become unimodal. However, it was also observed experimentally that many real-world ordinal data partly have values of the explanatory variable where the underlying CPD will be non-unimodal, and hence unimodal likelihood models may suffer from a bias for such a CPD. Therefore, motivated to mitigate such a bias, we propose approximately unimodal likelihood models, which can represent up to a unimodal CPD and a CPD that is close to be unimodal. We also verify experimentally that a proposed model can be effective for statistical modeling of ordinal data and OR tasks. Show Chinese abstract

Abstract: 序数回归（OR，也称为序数分类）是对序数数据的分类，其中潜在的目标变量是分类型的，并且被认为对于潜在的解释变量具有自然的序数关系。 成功OR模型的关键在于找到一种“自然序数关系”的数据结构，这种结构在许多序数数据中是共通的，并将其反映到这些模型的设计中。 一项最近的OR研究发现，许多现实世界的序数数据表现出一种趋势，即给定解释变量的一个值时目标变量的条件概率分布（CPD）通常是单峰的。 因此，一些先前的研究开发了单峰似然模型，在这些模型中，预测的CPD被保证为单峰的。 然而，实验观察也表明，许多现实世界的序数数据中存在解释变量的某些值，使得潜在的CPD不是单峰的，因此单峰似然模型可能在这样的CPD上出现偏差。 因此，为了减轻这种偏差，我们提出了近似单峰似然模型，这些模型可以表示最多为单峰的CPD以及接近单峰的CPD。 我们还通过实验验证了所提出的模型在序数数据的统计建模和OR任务中的有效性。