Persistent Homology in Statistical Model Building

统计模型构建中的持久同源性

• 批准号: EP/K036106/1
• 负责人: Hugo Maruri-Aguilar
• 金额: $ 2.77万
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK036106%2F1
• 关键词: Persistent; Homology; Statistical; Model; Building

Variable selection in statistical modelling is concerned with the question of choosing the most relevant explanatory variables from a potentially large set of candidates.The goal is to achieve a good fit between a model and data without including too many variables. The main objective of this project is to adapt methods from the topological theory of persistent homology in order to develop new variable selection techniques. The proposal combines model description from the point of view of computational algebra with statistical methods such as the Lasso technique and Bayesian model selection.Partners from network modeling, climate modeling and from robust engineering and design will provide data which will be used in case studies to assess the performance of the new methods. Also, the project will scope the use of software for combining topological and statistical algorithms, which will enable researchers to combine the different approaches without having to do extensive programming. Methodological results from this project have the potential to be applied to the analysis of large data sets in areas where the detection of interactions between explanatory variables is crucial.

统计建模中的变量选择涉及从潜在的大量候选变量中选择最相关的解释变量的问题，其目标是在不包括太多变量的情况下实现模型与数据之间的良好拟合。这个项目的主要目标是适应方法从拓扑理论的持续同源性，以发展新的变量选择技术。该提案将从计算代数的角度描述模型与Lasso技术和贝叶斯模型选择等统计方法相结合，来自网络建模、气候建模以及稳健工程和设计的合作伙伴将提供数据，用于案例研究，以评估新方法的性能。此外，该项目将扩大使用软件结合拓扑和统计算法的范围，这将使研究人员能够联合收割机结合不同的方法，而不必进行广泛的编程。该项目的方法学成果有可能应用于对解释变量之间的相互作用进行检测至关重要的领域的大型数据集进行分析。

项目成果

Optimal design for smooth supersaturated models

平滑过饱和模型的优化设计

• DOI: 10.1016/j.jspi.2013.11.014
• 发表时间: 2014
• 期刊: Journal of Statistical Planning and Inference
• 影响因子: 0.9
• 作者: Bates R