基于扑克牌式排序的贝叶斯序数回归与序贯偏好诱导

中文摘要 AI 辅助

基于扑克牌式排序的序数回归（DOR）从参考备选方案的排序中推断价值函数，其中决策者（DM）在连续等级之间插入空白卡片以表达偏好强度。DOR及其随机扩展（SMAA-DOR）将这些回答视为定义一组兼容价值函数的硬约束。我们提出B-DOR，这是DOR的一种概率重构，其中每对相邻等级产生一个序数观测，即声明的方向和卡片数量，通过累积链接似然建模，该似然将空白卡片数量与备选方案之间的潜在价值差异联系起来。提出了两种贝叶斯推断算法：BAYES-DOR通过哈密顿蒙特卡洛对整个后验分布进行采样；FTRL-DOR通过约束凸优化跟踪最大后验估计。此外，通过多步诱导过程，诱导可以分散在多个短会话中，从而减轻决策者的认知负担。两种算法对于预测都具有对数遗憾界，该界适用于任何决策者响应序列，并指导先验超参数的选择。一项涵盖768种配置的蒙特卡洛研究表明，准确度随会话数量增加而提高，空白卡片在偏好方向之外提供了显著信息，两种算法在不一致回答下均保持良好的性能，并且两者均优于DOR和SMAA-DOR。一个对意大利区域医疗保健绩效的示例应用证明了该方法在构建综合指标方面的实际适用性。

英文摘要

The Deck-of-cards-based Ordinal Regression (DOR) infers a value function from a ranking of reference alternatives in which the Decision Maker (DM) inserts blank cards between consecutive levels to express preference intensity. DOR, and its stochastic extension (SMAA-DOR), treat these answers as hard constraints defining a set of compatible value functions. We propose B-DOR, a probabilistic reformulation of DOR in which each pair of adjacent levels yields an ordinal observation, the declared direction and the number of cards, modelled through a cumulative-link likelihood that relates the number of blank cards to the latent value difference between alternatives. Two Bayesian inference algorithms are proposed: BAYES-DOR samples the whole posterior distribution by Hamiltonian Monte Carlo; FTRL-DOR tracks the maximum a posteriori estimate by constrained convex optimization. Moreover, through a multi-step elicitation process, elicitation can be spread over several short sessions reducing the cognitive burden on the DM. Both algorithms enjoy logarithmic regret bounds for prediction that hold for any sequence of DM responses and that guide the choice of the prior hyperparameters. A Monte Carlo study over 768 configurations shows that accuracy grows with the number of sessions, that blank cards add significant information over preference directions alone, that both algorithms maintain good performance under inconsistent answers, and that both outperform DOR and SMAA-DOR. An illustrative application to Italian regional healthcare performance demonstrates the practical applicability of the approach for building composite indicators.

发表机构

• Poznań University of Technology（波兹南理工大学）
• University of Catania（卡塔尼亚大学）

机构由 AI 辅助整理，请以论文原文为准。