Collaborative Research: Bayesian Inference for Interpretable Random Structures

数据科学中的许多挑战性问题都可以通过对患者、客户、蛋白质、症状或其他实验单位的随机子集进行推断来表征。例如，搜索从给定治疗中获益最多的患者亚群，识别表征不同肿瘤细胞亚群的突变子集，然后可以作为可能的治疗靶点，或者发现电子健康记录中的潜在疾病模式，可以用于提出改进的资源分配。 在所有三个例子中，推理目标作为随机子集的不寻常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一数字的推断目标，如治疗效果，差异蛋白质表达水平或平均反应。 本项目旨在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推理问题，从而弥补目前可用方法中的这一差距。本项目通过明确引入简约性和可解释性作为报告推理的标准，为随机子集开发新的统计推理方法，以解决此类推理问题。相关的方法开发的随机分区，功能分配，并扩展这样的结构。除了模型和推理范式的发展，拟议的工作的第二个主要推力是计算上可行的实现大型数据集的发展。当使用模拟精确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的实现。虽然在最近的文献中已经开发了几种用于全局参数的大数据后验模拟方法，但是很少有用于随机子集的这样的方法，即，局部参数这个奖项反映了NSF的法定使命，并被认为是值得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的支持。

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.