Prediction becomes more challenging with missing covariates. What method is chosen to handle missingness can greatly affect how models perform. In many real-world problems, the best prediction performance is achieved by models that can leverage the informative nature of a value being missing. Yet, the reasons why a covariate goes missing can change once a model is deployed in practice. If such a missingness shift occurs, the conditional probability of a value being missing differs in the target data. Prediction performance in the source data may no longer be a good selection criterion, and approaches that do not rely on informative missingness may be preferable. However, we show that the Bayes predictor remains unchanged by ignorable shifts for which the probability of missingness only depends on observed data. Any consistent estimator of the Bayes predictor may therefore result in robust prediction under those conditions, although we show empirically that different methods appear robust to different types of shifts. If the missingness shift is non-ignorable, the Bayes predictor may change due to the shift. While neither approach recovers the Bayes predictor in this case, we found empirically that disregarding missingness was most beneficial when it was highly informative.
ICYM2I: The illusion of multimodal informativeness under missingness
Department of Biomedical Informatics, Columbia University（生物医学信息学系，哥伦比亚大学）；Seymour, Paul, and Gloria Milstein Division of Cardiology, Department of Medicine, Columbia University Irving Medical Center（塞缪尔、保罗和格洛丽亚米尔斯坦心脏病科，哥伦比亚大学伊万格琳医学中心）
AdapDISCOM: An Adaptive Sparse Regression Method for High-Dimensional Multimodal Data With Block-Wise Missingness and Measurement Errors
Institut national de la recherche scientifique (INRS)（国家科学研究研究所）；Université du Québec à Chicoutimi (UQAC)（魁北克大学希库蒂米分校）；McGill University（麦吉尔大学）；The Neuro (Montreal Neurological Institute-Hospital)（蒙特利尔神经学研究所/医院）；Douglas Hospital Research Centre（道格拉斯医院研究中心）
Causal Effect Estimation with TMLE: Handling Missing Data and Near-Violations of Positivity
Ludwig-Maximilians University Munich（路德维希-马克西米利安慕尼黑大学）；Centre for Integrated Data and Epidemiological Research（综合数据与流行病学研究中心）；UMIT - University for Health Sciences, Medical Informatics and Technology（UMIT - 健康科学、医学信息与技术大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
缺失值的存在使得监督学习更具挑战性。事实上，以前的工作已经表明，即使响应是完整数据的线性函数，最佳预测器也是观察到的条目和缺失指标的复函数。因此，一致性方法的计算或样本复杂性取决于缺失模式的数量，其在维度数量上可以是指数级的。在这项工作中，我们推导出线性假设和各种缺失数据机制，包括随机缺失（MAR）和自屏蔽（Missing Not At Random）下的最佳预测的分析形式。基于Neumann级数近似的最优预测，我们提出了一个新的原则架构，命名为NeuMiss网络。它们的独创性和力量来自于使用一种新型的非线性：乘以缺失指标。我们提供了一个上限NeuMiss网络的贝叶斯风险，并表明他们有良好的预测精度与一些参数和独立的缺失数据模式的数量的计算复杂性。因此，它们可以很好地扩展到具有许多特征的问题，并且对于中等大小的样本仍然具有统计效率。此外，我们表明，相反的程序使用EM或插补，他们是强大的缺失数据机制，包括困难的MNAR设置，如自屏蔽。
