Identification and Statistical Inference in Graphical Models with Feedback and Latent Variables

在过去的十年里，科学实验取得了巨大的进步。例如，在生物学中，收集同时量化许多基因或蛋白质表达水平的复杂数据已经成为一种惯例。该项目涉及统计方法的发展，以便能够处理这类数据，以便深入了解所研究的系统中各单位之间的因果关系。具体地说，拟议的研究解决了两个关键挑战，即如何处理一些重要变量仍未被观察到的问题，以及如何应对因果反馈循环的存在。这项研究发展了统计技术来推断因果关系，并扩大了我们对不完全信息下可能得出的结论的理解。反馈和潜在变量都给图形建模带来了巨大的挑战，因为在它们存在的情况下，考虑条件独立性不再足以刻画和比较模型。该项目侧重于线性模型，该模型允许对反馈回路和/或潜在变量的影响进行精细建模。PI将制定参数可辨识性的标准，这不再由反馈或潜在变量来保证。这项工作还将确定模型何时具有由参数计数给定的预期尺寸的条件。例如，在统计检验中设置自由度时，需要维度知识。接下来，该项目将导致对条件独立以外的约束的更好理解。最后，PI将在高斯和非高斯模型中开发新的模型选择方法。

The last decade has seen great advances in scientific experimentation. In biology, for instance, it has become routine to collect complex data that simultaneously quantify the levels of expression of many genes or proteins. This project addresses the development of statistical methodology that allows processing of such data to obtain insights on cause-effect relationships among the units in the studied system. Specifically, the proposed research addresses two key challenges, namely, how to tackle problems in which some important variables remain unobserved, and how to cope with the presence of causal feedback loops. The research develops statistical techniques to infer cause-effect relationships and expands our understanding of which conclusions may possibly be reached under imperfect information.Both feedback and latent variables bring about great challenges in graphical modeling because, in their presence, consideration of conditional independence is no longer sufficient to characterize and compare models. This project focuses on linear models that allow for refined modeling of feedback loops and/or the effects of latent variables. The PI will develop criteria for parameter identifiability, which is no longer guaranteed with feedback or latent variables. The work will also determine conditions for when a model is of expected dimension as given by a parameter count. Knowledge of dimension is needed for instance when setting degrees of freedom in statistical tests. Next, the project will lead to a better understanding of constraints other than conditional independence. Finally, the PI will develop new model selection methods in Gaussian as well non-Gaussian models.