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常规。 该项目致力于统计方法的发展，允许处理这些数据，以了解研究系统中各单位之间的因果关系。 具体来说，拟议的研究解决了两个关键的挑战，即，如何解决一些重要的变量仍然未观察到的问题，以及如何科普因果反馈回路的存在。 该研究开发了统计技术来推断因果关系，并扩大了我们的理解，可能会得出结论下不完美的information.Both反馈和潜变量带来了巨大的挑战，在图形建模，因为在他们的存在，考虑条件独立性不再足以表征和比较模型。 这个项目的重点是线性模型，允许反馈回路和/或潜在变量的影响的精细建模。 PI将制定参数可识别性的标准，这不再通过反馈或潜变量来保证。 这项工作还将确定当模型具有由参数计数给出的预期尺寸时的条件。 例如，在统计检验中设置自由度时，需要维度知识。 接下来，该项目将导致更好地理解条件独立性以外的约束。 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.