As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom. We show that the PCMC model significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on both synthetic and empirical datasets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.
翻译:随着获取人类选择的数据集在丰富性和规模上不断增长 -- -- 特别是在在线领域 -- -- 越来越需要摆脱常规、随机中转性和露西的选择轴等传统选择-理论轴的选用模型。 在这项工作中,我们引入了“Pairwise选择 Markov 链” 的离散选择模式,这是一种不假定以上任何轴心的必然可移动模型,同时仍然满足统一扩展的基本轴心,这一假设比露西的选择轴心要弱得多。我们表明,PCMC模型在合成和实验数据集的预测任务中明显优于多数值逻辑模型(MNL),而已知这些数据集显示卢西的反正轴。我们的分析还综合了将多数值逻辑模型与Markov链连接起来的最近几次观测;PCMC模型保留了多数值日志模型作为特例。