Pair-Matching：基于自适应查询的链接预测
Pair-Matching: Links Prediction with Adaptive Queries
AI总结：
本文研究单次查询约束下的配对匹配链接预测问题，在两社群SBM图结构中证明可达到次线性遗憾，给出与Kesten-Stigum阈值相关的最优界，并分析节点采样限制及多社群猜想。
摘要：
配对匹配问题出现在许多应用中，人们希望在这些应用中发现实体或个体之间的良好匹配。形式上，个体集合由图的节点表示，其中最初未被观测到的边代表良好匹配。算法查询节点对，并观测边的存在与否。其目标是在固定的查询预算内发现尽可能多的边。配对匹配是多臂老虎机问题的一个特定实例，其中臂是个体对，奖励是连接这些个体对的边。不过，这一老虎机问题是非标准的，因为每个臂只能被拉动一次。鉴于后一约束，只有当图呈现某种底层结构时，才能期望获得次线性遗憾。本文表明，当图根据具有两个社群的随机块模型（SBM）生成时，可以实现次线性遗憾。文中为该配对匹配问题计算了最优遗憾界。这些遗憾界展现出与SBM中社群检测的Kesten-Stigum阈值相关的相变。本文还考虑了每个节点被约束为采样次数少于给定次数情况下的配对匹配问题。我们展示了最优遗憾率如何依赖于这一约束。论文最后提出了一个关于社群数量大于2时最优遗憾的猜想。与两个社群的情况相反，我们认为该问题中会出现统计—计算差距。
英文摘要：
The pair-matching problem appears in many applications where one wants to discover good matches between pairs of entities or individuals. Formally, the set of individuals is represented by the nodes of a graph where the edges, unobserved at first, represent the good matches. The algorithm queries pairs of nodes and observes the presence/absence of edges. Its goal is to discover as many edges as possible with a fixed budget of queries. Pair-matching is a particular instance of multi-armed bandit problem in which the arms are pairs of individuals and the rewards are edges linking these pairs. This bandit problem is non-standard though, as each arm can only be played once. Given this last constraint, sublinear regret can be expected only if the graph presents some underlying structure. This paper shows that sublinear regret is achievable in the case where the graph is generated according to a Stochastic Block Model (SBM) with two communities. Optimal regret bounds are computed for this pair-matching problem. They exhibit a phase transition related to the Kesten-Stigum threshold for community detection in SBM. The pair-matching problem is considered in the case where each node is constrained to be sampled less than a given amount of times. We show how optimal regret rates depend on this constraint. The paper is concluded by a conjecture regarding the optimal regret when the number of communities is larger than 2. Contrary to the two communities case, we argue that a statistical-computational gap would appear in this problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
