RI: Small: Inference with Incomplete Data

数据缺失是困扰经验主义科学每一个分支的问题。传感器并不总是可靠地工作，受访者不会填写问卷中的每一个问题，内科患者往往无法回忆起事件、治疗或结果。这个项目试图通过对可能导致一些数据丢失和其他数据被观察的过程进行推理，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种过程，并确定从缺失数据中恢复的条件是可行的，如果是这样的话，如何恢复。该项目将侧重于现有技术认为回收不可行的条件。通过学习如何管理这些条件，这项研究将有利于包括机器学习、大数据、流行病学、统计学、经济学、社会科学和医学在内的多个领域的实证研究。拟议的研究的目的是开发能够通过在图形因果模型中编码假设来从不完整数据中学习的计算机系统。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，这项研究将制定有效的程序，以确定是否可以在不完整数据的情况下计算统计和因果关系的无偏估计，以及促进这种估计的假设是否具有可检验的影响。此外，它还将为那些被证明是不可估量的关系产生界限。这些反过来将导致在理论上理解在缺失数据条件下什么是可能的，什么是不可能的。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.