Causal Matrix Completion
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AI 根据所提供的论文材料归类：摘要以潜在结果定义因果矩阵补全问题，并提出因果目标量的识别与估计方法。
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因果矩阵补全
- 研究问题
- 论文研究未观测因素同时决定矩阵元素与观测缺失模式时，如何在非随机缺失数据中识别并估计因果目标量及缺失矩阵元素。
- 方法与思路
- 作者用潜在结果建立矩阵补全的因果模型，提出相应识别论证和合成最近邻估计程序，并分析有限样本及渐近统计性质。
- 材料陈述的贡献
- 摘要称建立估计量的有限样本一致性和渐近正态性，并给出非随机缺失下逐元素、最大范数意义的结果，完全随机缺失为特例。
- 阅读关注点
- 阅读全文时应核对非随机缺失下的具体识别限制、合成邻居的构造与数据支持要求，以及有限样本界和渐近结果的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要未说明识别条件及界的具体形式，不能理解为任意非随机缺失都可恢复。
原文摘要
Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are "missing completely at random" (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of "latent confounders", i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix. For example, in the context of movie recommender systems -- a canonical application for matrix completion -- a user who vehemently dislikes horror films is unlikely to ever watch horror films. In general, these confounders yield "missing not at random" (MNAR) data, which can severely impact any inference procedure that does not correct for this bias. We develop a formal causal model for matrix completion through the language of potential outcomes, and provide novel identification arguments for a variety of causal estimands of interest. We design a procedure, which we call "synthetic nearest neighbors" (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.