RI: Small: Inference with Incomplete Data

缺失数据是困扰实证科学每个分支的问题。传感器并不总是可靠地工作，受访者并没有填写问卷中的每一个问题，医疗患者往往无法回忆起事件，治疗或结果。该项目试图通过推理可能导致一些数据丢失和其他数据被观察到的过程，从部分观察到的数据中恢复感兴趣的信息。图形模型和因果推理的最新进展使我们能够正式描述这些过程，并确定条件下，从丢失的数据恢复将是可行的，如果是这样，如何。该项目将侧重于被认为利用现有技术无法进行回收的情况。通过学习管理这种情况下，这项研究将有利于在各种领域的实证研究，包括机器学习，大数据，流行病学，统计学，经济学，社会科学和medicine.The拟议的研究的目的是开发计算机系统能够从不完整的数据通过编码的假设在图形因果模型学习。使用这样的模型，我们将确定促进（或禁止）推理和学习的条件。特别是，本研究将制定有效的程序，以确定是否无偏估计的统计和因果关系，可以计算不完整的数据，以及是否有利于这种可估计性的假设有可检验的影响。此外，它将为那些被证明是不可估量的关系生成边界。这些反过来又会导致对缺失数据条件下什么是可能的和不可能的理论理解。鉴于数据缺失问题的普遍存在，我们相信这项研究将为所有数据密集型科学创造新的重要工具。

Missing data is a problem that plagues every branch of empirical science. Sensors do not always work reliably, respondents do not fill out every question in the questionnaire, and medical patients are often unable to recall episodes, treatments or outcomes. This project attempts to recover information of interest from partially observed data by reasoning about the process that could have caused some data to be missing and others to be observed. Recent advances in graphical models and causal inference permit us to describe such processes formally and identify conditions under which recovery from missing data would be feasible and, if so, how. This project will focus on conditions in which recovery is deemed infeasible by available techniques. By learning to manage such conditions this research will benefit empirical research in a variety of fields, including machine learning, big data, epidemiology, statistics, economics, social science and medicine.The aim of the proposed research is to develop computer systems capable of learning from incomplete data by encoding assumptions in a graphical causal model. Using such models we will identify conditions that facilitate (or prohibit) inference and learning. In particular, this research will develop effective procedures for determining whether unbiased estimates of statistical and causal relationships can be computed given incomplete data and whether assumptions that facilitate such estimability have testable implications. Additionally, it will generate bounds for those relationships that are proved to be inestimable. These will in turn lead to a theoretical understanding of what is possible and impossible under missing data conditions. Given the ubiquity of the missing data problem we believe this research will create new and important tools for all data-intensive sciences.