研究在参数假设下如何选择评分规则权重，以更准确估计目标统计量。
Choice of Scoring Rules for Indirect Elicitation of Properties with Parametric Assumptions
- 通过加权多个可直接诱发的子属性评分规则，间接估计目标属性。
- 实验发现权重单调变化时目标估计值随之单调变化，最优解常为部分权重为零。
- 理论证明二维情形下权重影响可被精确解释，高维情形可用线性近似分析。
人们常关注随机事件的统计属性（如均值、方差）预测。合适的评分规则能评估预测质量，要求其期望得分在真实预测处唯一最大化，此时称该评分规则可直接诱发该属性。已有研究多关注不同属性对应的评分规则存在性与表征，但对实际应用中如何选择评分规则讨论较少。本文探讨一种新任务：在参数假设下的间接诱发属性，即目标属性是若干可直接诱发子属性的函数，总评分是各子属性对应评分规则的加权和。由于限制在特定参数模型类中，不同权重设置导致不同的约束最优解。研究目标是理解权重选择如何影响目标属性估计，并确定最佳配置。通过模拟实验发现，多数情况下目标属性的最优估计随各权重增加而单调变化，且最优权重配置常为部分权重为零。为理解机制，先建立基本理论框架，再分别给出二维及高维情形的充分条件。二维理论完全解释了实验结果；高维情形中特别研究线性情况，建议当真实子属性值足够接近参数空间时，可通过局部映射或线性近似理解复杂设定。
原文摘要 · Abstract (English)
People are commonly interested in predicting a statistical property of a random event such as mean and variance. Proper scoring rules assess the quality of predictions and require that the expected score gets uniquely maximized at the precise prediction, in which case we call the score directly elicits the property. Previous research work has widely studied the existence and the characterization of proper scoring rules for different properties, but little literature discusses the choice of proper scoring rules for applications at hand. In this paper, we explore a novel task, the indirect elicitation of properties with parametric assumptions, where the target property is a function of several directly-elicitable sub-properties and the total score is a weighted sum of proper scoring rules for each sub-property. Because of the restriction to a parametric model class, different settings for the weights lead to different constrained optimal solutions. Our goal is to figure out how the choice of weights affects the estimation of the target property and which choice is the best. We start it with simulation studies and observe an interesting pattern: in most cases, the optimal estimation of the target property changes monotonically with the increase of each weight, and the best configuration of weights is often to set some weights as zero. To understand how it happens, we first establish the elementary theoretical framework and then provide deeper sufficient conditions for the case of two sub-properties and of more sub-properties respectively. The theory on 2-D cases perfectly interprets the experimental results. In higher-dimensional situations, we especially study the linear cases and suggest that more complex settings can be understood with locally mapping into linear situations or using linear approximations when the true values of sub-properties are close enough to the parametric space.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。