Inference for Stationary Processes: Optimal Transport and Generalized Bayesian Approaches

这个项目将解决对观测序列进行推断的问题，这些序列表现出由物理或其他相互作用引起的依赖性。这类观察出现在许多领域，包括金融、生态学、自然语言处理和生物学。我们将探索利用最优运输理论的思想将一系列观测结果拟合到一系列统计模型中的方法。非正式地，我们将确定家族中的模型，其中观察的生成机制可以以最小的总成本转换。我们将讨论这些转化成本的理论和有效计算，并将考虑在生物医学和计算机科学中的应用。该项目将涉及与研究生和更多从事基因组学和生物信息学工作的高级研究人员的合作。本科生和研究生都将通过参与支持的研究项目接受培训。在更技术性的层面上，该项目将解决随机过程的推理，特别是如何将一组平稳过程拟合到一个观察到的遍历过程中，依次揭示。研究将侧重于最优运输思想的使用和扩展，包括固定过程和相关变分量的固定耦合，重点是方法开发和支持理论。这项研究有两个主要目的。第一个目的是研究基于连接的最小散度估计，包括熵正则化的使用和性质。第二个目标是研究马尔可夫链最优转移耦合的有效计算，并将其应用于图距离、图对齐和隐马尔可夫模型。该项目将涉及与研究生和更多从事基因组学和生物信息学工作的高级研究人员的合作。本科生和研究生都将通过参与支持的研究项目接受培训。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will address the problem of making inferences about sequences of observations that exhibit dependence arising from physical or other interactions. Observations of this sort occur in many fields, including finance, ecology, natural language processing, and biology. We will explore ways to fit a sequence of observations to a family of statistical models using ideas from the theory of optimal transport. Informally, we will identify models in the family into which the generating mechanism of the observations can be transformed with the least overall cost. We will address both the theory and efficient computation of these transformation costs, and will consider applications to biomedicine and computer science. The project will involve collaborations with graduate students and more senior researchers working in genomics and bioinformatics. Both undergraduate and graduate students will receive training through involvement in supported research projects.On a more technical level, this project will address inference for stochastic processes, in particular, how to fit a family of stationary processes to an observed ergodic process, revealed sequentially. Research will focus on the use and extension of ideas from optimal transport, including stationary couplings of stationary processes and related variational quantities, with a focus on methods development and supporting theory. The research has two primary aims. The first aim is to investigate minimum divergence estimation based on joinings, including the use and properties of entropy regularization. The second aim is to investigate the efficient computation of optimal transition couplings of Markov chains, with applications to graph distances, graph alignment, and hidden Markov models. The project will involve collaborations with graduate students and more senior researchers working in genomics and bioinformatics. Both undergraduate and graduate students will receive training through involvement in supported research projects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.