提出抗克隆权重机制，防止相似数据重复导致的偏差。
Clone-Robust Weights in Metric Spaces: Handling Redundancy Bias for Benchmark Aggregation
- 设计克隆鲁棒的加权函数，使相似元素共享权重
- 在欧氏空间中证明此类权重函数存在并可构造
- 适用于基准聚合、领域自适应等需防冗余场景
给定度量空间中的一组元素，其分布可能任意甚至对抗性。能否设计一种对这类操纵具有鲁棒性的加权方式？该问题出现在多个场景中：元素可代表需稳健领域自适应的数据点，或需聚合为基准的任务；亦可表示投票建议应用中的政治观点问题。本文提出理论框架，引入克隆鲁棒加权函数作为解法概念。这类函数将重要性分配给集合中的元素，使得相似对象（“克隆”）共享部分权重，从而避免因重复带来的偏差。框架将最大不确定性原理扩展至一般度量空间，并提出对称性、连续性和克隆鲁棒性三类公理以指导加权函数构造。最后，我们解决了欧氏空间中满足这些公理的加权函数的存在性问题，并提出一种通用构造方法。
原文摘要 · Abstract (English)
We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations? This problem arises in various contexts. For instance, the elements could represent data points, requiring robust domain adaptation. Alternatively, they might represent tasks to be aggregated into a benchmark; or questions about personal political opinions in voting advice applications. This article introduces a theoretical framework for dealing with such problems. We propose clone-proof weighting functions as a solution concept. These functions distribute importance across elements of a set such that similar objects (``clones'') share (some of) their weights, thus avoiding a potential bias introduced by their multiplicity. Our framework extends the maximum uncertainty principle to accommodate general metric spaces and includes a set of axioms -- symmetry, continuity, and clone-proofness -- that guide the construction of weighting functions. Finally, we address the existence of weighting functions satisfying our axioms in the significant case of Euclidean spaces and propose a general method for their construction.
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