Vector-Valued Property Elicitation
Vector-Valued Property Elicitation
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向量值属性导出
DOI：
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发表时间：
2015
期刊：
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通讯作者：
Ian A. Kash
中科院分区：
文献类型：
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作者：
Rafael M. Frongillo;Ian A. Kash
统计数据或分布属性的提取是设计适当的评分规则的任务，相当于适当的损失，这激励代理或算法真实地估计潜在概率分布或数据集的期望属性。利用启发和凸分析之间的联系，我们解决了向量值属性案例，尽管它应用于机器学习和统计学，但在文献中很少受到关注。我们首先提供了线性和线性比率性质的非常一般的表征，其中第一个通过统一和加强机器学习和统计学中先前的几个表征来解决一个开放的问题。然后，我们询问哪些属性向量允许不可分离的分数，这些分数不能单独表示为每个坐标的分数之和，这是机器学习的自然愿望。我们表明线性和线性比率确实承认不可分的分数，并为一个猜想提供证据，即这些是唯一这样的性质（直到链接函数）。最后，我们给出了一种产生识别函数的一般方法，并通过表明凸最大水平集在一般情况下不足以满足适宜性来解决一个开放问题。
The elicitation of a statistic, or property of a distribution, is the task of devising proper scoring rules, equivalently proper losses, which incentivize an agent or algorithm to truthfully estimate the desired property of the underlying probability distribution or data set. Leveraging connections between elicitation and convex analysis, we address the vector-valued property case, which has received little attention in the literature despite its applications to both machine learning and statistics. We first provide a very general characterization of linear and ratio-of-linear properties, the first of which resolves an open problem by unifying and strengthening several previous characterizations in machine learning and statistics. We then ask which vectors of properties admit nonseparable scores, which cannot be expressed as a sum of scores for each coordinate separately, a natural desideratum for machine learning. We show that linear and ratio-of-linear do admit nonseparable scores, and provide evidence for a conjecture that these are the only such properties (up to link functions). Finally, we give a general method for producing identification functions and address an open problem by showing that convex maximal level sets are insufficient for elicitability in general.