提出近似单峰似然模型，更好建模真实有序数据分布。
Approximately Unimodal Likelihood Models for Ordinal Regression
- 设计可容纳近似单峰的似然函数，放宽严格单峰限制。
- 实验表明在真实有序数据上优于传统单峰模型。
- 适合处理具有局部非单峰特性的有序回归任务。
有序回归（Ordinal Regression, OR）是针对具有自然序关系的分类问题。成功的关键在于发现并建模普遍存在的“自然序关系”结构。近期研究发现，许多真实世界的有序数据其条件概率分布（CPD）常呈单峰特征。已有方法构建了保证预测CPD单峰的模型，但实验显示部分真实数据中存在非单峰的解释变量取值，导致单峰模型产生偏差。为此，本文提出近似单峰似然模型，可表示严格单峰或接近单峰的分布，提升对复杂实际数据的适应能力。实验验证该模型在统计建模与有序回归任务中均具有效性。
原文摘要 · Abstract (English)
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.
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