We develop a conformal inference method to construct joint confidence regions for structured groups of missing entries within a sparsely observed matrix. This method is useful to provide reliable uncertainty estimation for group-level collaborative filtering; for example, it can be applied to help suggest a movie for a group of friends to watch together. Unlike standard conformal techniques, which make inferences for one individual at a time, our method achieves stronger group-level guarantees by carefully assembling a structured calibration data set mimicking the patterns expected among the test group of interest. We propose a generalized weighted conformalization framework to deal with the lack of exchangeability arising from such structured calibration, and in this process we introduce several innovations to overcome computational challenges. The practicality and effectiveness of our method are demonstrated through extensive numerical experiments and an analysis of the MovieLens 100K data set.

翻译：我们提出了一种共形推断方法，用于为稀疏观测矩阵中缺失条目的结构化群体构造联合置信区域。该方法可为群体层面的协同过滤提供可靠的置信度估计；例如，它可被应用于帮助为一群朋友共同观看的电影推荐建议。与每次对单个个体进行推断的标准共形技术不同，我们的方法通过精心构建一个模拟目标测试群体预期模式的结构化校准数据集，实现了更强的群体层面保证。我们提出了一种广义加权共形化框架，以处理此类结构化校准时出现的非可交换性问题，并在这一过程中引入了若干创新来克服计算挑战。通过大量数值实验以及对MovieLens 100K数据集的分析，我们验证了该方法的实用性和有效性。