Persistent Homology in Statistical Model Building

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。目标是在不包含太多变量的情况下实现模型和数据之间的良好拟合。本项目的主要目标是适应持续同源拓扑理论的方法，以开发新的变量选择技术。该方案从计算代数的角度将模型描述与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，这些数据将用于案例研究，以评估新方法的性能。此外，该项目还将使用结合拓扑和统计算法的软件，这将使研究人员能够结合不同的方法，而无需进行大量的编程。这个项目的方法学结果有可能应用于对解释变量之间相互作用的检测至关重要的领域的大型数据集的分析。

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.