Inference for Stationary Processes: Optimal Transport and Generalized Bayesian Approaches

这个项目将解决对因物理或其他相互作用而表现出相关性的观察序列进行推断的问题。这类观测出现在许多领域，包括金融、生态、自然语言处理和生物学。我们将利用最优运输理论的思想，探索将一系列观测数据与一系列统计模型相匹配的方法。非正式地，我们将在家族中确定可以以最小的总体成本将观测的生成机制转换成的模型。我们将讨论这些转换成本的理论和有效计算，并将考虑将其应用于生物医学和计算机科学。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来接受培训。在更技术性的水平上，这个项目将讨论随机过程的推理，特别是如何将一族平稳的过程与观察到的遍历过程进行匹配，按顺序揭示。研究将侧重于最优运输思想的使用和推广，包括平稳过程和相关变化量的平稳耦合，重点是方法开发和支持理论。这项研究有两个主要目的。第一个目标是研究基于联合的最小散度估计，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的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NSF的法定使命，并通过使用基金会的智力优势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.