Collaborative Research: Bayesian Inference for Interpretable Random Structures

数据科学中的许多具有挑战性的问题可以描述为对患者、客户、蛋白质、症状或其他实验单位的随机子集的推断。例如，寻找从特定治疗中受益最多的患者亚群，确定表征不同肿瘤细胞亚群的突变亚集，然后作为可能的治疗目标，或者在电子健康记录中发现潜在的疾病模式，可用于提出改进资源分配的建议。在这三个例子中，推理目标作为随机子集的不同寻常的性质引起了具有挑战性的数据分析问题。相比之下，大多数传统方法适用于单个数字的推断目标，如治疗效果、差异蛋白表达水平或平均反应。这个项目的目的是通过开发和应用新的方法来解决与随机子集相关的几个特定的推理问题，以弥补现有方法中的这一差距。该项目开发了新的随机子集统计推理方法，通过明确地引入简约性和可解释性作为报告推理的标准来处理这些推理问题。开发了用于这种结构的随机划分、特征分配和扩展的相关方法。除了开发模型和推理范例外，拟议工作的第二个主要主题是为大数据集开发在计算上可行的实现。当使用模拟精确的后验蒙特卡罗方法时，随机子集的基于模型的贝叶斯推理很快导致计算密集型实现。虽然最近的文献中已经提出了几种全局参数的大数据后验模拟方法，但对于随机子集，即局部参数，这种方法还很少。该项目将探索开发这种方法的几种方法。这一奖项反映了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。

Many challenging questions in data science can be characterized in terms of inference for random subsets of patients, customers, proteins, symptoms, or other experimental units. Examples include the search for a subpopulation of patients who most benefit from a given treatment, the identification of subsets of mutations that characterize different tumor cell subpopulations that could then serve as possible treatment targets, or the discovery of latent disease patterns in electronic health records that could be used to propose an improved allocation of resources. In all three examples, the unusual nature of the inference targets as random subsets gives rise to challenging data analysis problems. In contrast, most traditional methods work for inference targets that are a single number, like a treatment effect, a level of differential protein expression, or a mean response. This project aims to address this gap in currently available methodology by developing and applying new methods to solve several specific inference problems related to random subsets.This project develops novel statistical inference methods for random subsets to approach such inference problems by explicitly introducing parsimony and interpretability as criteria for the reported inference. Related methods are developed for random partitions, feature allocation, and extensions of such structures. Besides the development of models and inference paradigms, a second major thrust of the proposed work is the development of computationally feasible implementations for large data sets. Model-based Bayesian inference for random subsets quickly leads to prohibitively computation-intensive implementations when simulation-exact posterior Monte Carlo methods are used. While several big data posterior simulation methods for global parameters have been developed in recent literature, there are few such methods for random subsets, i.e., local parameters. The project will explore several approaches to develop such methods.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.