Collaborative Research: Selection Methods for Algebraic Design of Experiments

协作研究：实验代数设计的选择方法

• 批准号: 1937717
• 负责人: Elena Dimitrova
• 金额: $ 6.39万
• 依托单位: California Polytechnic State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-05-02 至 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1937717&HistoricalAwards=false
• 关键词: Collaborative; Research; Selection; Methods; Algebraic

Data science has emerged as an important field for making decisions based on data collected from sectors as varied as healthcare and housing. Though data are plentiful, thanks to phone apps, merchant loyalty cards, and social media accounts, there is still a question of whether more data translates to more knowledge. Furthermore collection and storage can be problematic especially when data are sensitive, as it is often the case with clinical trials and genetic experiments. The problem of selecting information-rich data becomes crucial for creating models that can reliably predict the outcome of future experiments. Few results have been published on the amount of necessary data, and currently there are no guidelines for generating specific data sets which would unambiguously identify a predictive model. As a first step towards developing a complete theory, the PIs will focus on models described by finite-valued nonlinear polynomial functions. (For example, the internal "function" in WedMD's Symptom Checker returns medical conditions according to symptoms input by the user.) They will construct the smallest data sets that have a single associated polynomial model and study properties of such data sets. From these computational experiments, they will build the appropriate theory, design algorithms, and generate code that can be later developed into software complete with a graphical user interface. Graduate students will participate at the appropriate level of each component of the project. Such an experience will provide them possible topics for an MS or PhD dissertation and will very likely inspire a career-long involvement in the STEM disciplines. The theoretical results will advance the fields of design of experiments, network inference, and finite dynamical systems through the determination of criteria for selecting data sets to uniquely identify models. The algorithms will serve as a guide for experimentalists in determining the data that are needed to identify the structure of a network of interest. Such knowledge has the potential to drastically reduce wasted resources that arise from too much data with too little information.While this is the age of big data, there is still a question of whether more data translates to more knowledge. Particularly when collecting data is expensive or time consuming, as it is often the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models. Finite-state multivariate polynomial functions have successfully been used to model complex networks from discretized data; however, few results have been published on the amount of data necessary for such models, with the majority applying to Boolean models only. It is still unknown which data points explicitly identify such discrete models, and as a consequence, there are no methods for generating the specific data sets which would unambiguously identify the model. The PIs will address the issue of the minimality and specificity of data to uniquely identify discrete polynomial models by developing the appropriate theory, designing algorithms, and generating code that can be later built into software. Graduate students will participate at the appropriate level of each component of the project. This project will resolve some important computational issues in network inference and will improve experimental design and model selection by eliminating the effect of computational artifacts that arise when working with nonlinear multivariate polynomials. The theoretical results will advance the fields of design of experiments and network inference through the establishment of criteria to select data sets to uniquely identify models. The proposed work will also increase the utility of polynomial dynamical systems as models of complex networks by establishing the minimal amount of the data for unique model identification. The algorithms will serve as a guide for experimentalists in determining the data that are needed to identify the structure of a network of interest. Such knowledge has the potential to drastically reduce the number of experiments performed and to eliminate the generation of data with little intrinsic value.

数据科学已成为基于从医疗保健和住房等不同部门收集的数据做出决策的重要领域。 尽管数据很丰富，这要归功于电话应用程序，商户忠诚度卡和社交媒体帐户，但仍然存在一个问题，即是否有更多数据转化为更多知识。此外，收集和存储可能是有问题的，尤其是当数据敏感时，临床试验和基因实验通常是这种情况。 选择信息丰富的数据的问题对于创建可以可靠地预测未来实验结果的模型至关重要。关于必要数据数量的结果很少，目前尚无生成特定数据集的准则，这些数据集可以明确识别预测模型。作为发展完整理论的第一步，PI将重点关注有限价值的非线性多项式函数所描述的模型。 （例如，WEDMD症状检查器中的内部“功能”根据用户输入的症状返回医疗状况。）他们将构建具有单个相关的多项式模型和此类数据集的研究属性的最小数据集。 从这些计算实验中，它们将构建适当的理论，设计算法并生成代码，以后可以将其开发为具有图形用户界面的软件。研究生将参加项目的每个组成部分的适当水平。这样的经历将为他们提供MS或博士学位论文的可能主题，并很可能会激发职业生涯的长期参与。理论结果将通过确定选择数据集以唯一识别模型的标准来推进实验，网络推理和有限动态系统的设计领域。该算法将作为实验者的指南，以确定确定感兴趣网络的结构所需的数据。这种知识有可能大幅度减少来自太多信息的数据，而信息太少。虽然这是大数据的时代，但仍然存在一个问题，即是否有更多的数据转化为更多的知识。尤其是当收集数据昂贵或耗时时，临床试验和生物分子实验通常是这种情况，选择富含信息的数据的问题对于创建相关模型至关重要。有限状态多元多项式函数已成功地用于从离散数据中对复杂网络进行建模。但是，关于此类模型所需的数据量的结果很少，大多数仅适用于布尔模型。仍然未知哪些数据点明确识别此类离散模型，因此，没有方法可以生成特定的数据集，这些数据集将明确识别模型。 PI将通过开发适当的理论，设计算法和生成可以稍后内置到软件中的代码来解决数据的最小和特异性问题，以唯一识别离散多项式模型。研究生将参加项目的每个组成部分的适当水平。该项目将解决网络推理中的一些重要计算问题，并通过消除使用非线性多元多项式工作时会产生的计算伪像的效果来改善实验设计和模型选择。理论结果将通过建立标准来选择数据集以唯一识别模型，从而推进实验和网络推断的设计领域。提出的工作还将通过确定唯一模型标识的数据量最小的数据来增加多项式动力学系统作为复杂网络的模型的实用性。该算法将作为实验者的指南，以确定确定感兴趣网络的结构所需的数据。这种知识有可能大幅度减少执行的实验数量，并消除几乎没有内在值的数据的产生。

项目成果

Gröbner Bases of Convex Neural Code Ideals

凸神经代码理想的 Gröbner 基

• DOI: 10.1007/978-3-030-42687-3_8
• 发表时间: 2020
• 期刊: Advances in mathematical sciences
• 作者: Kaitlyn Phillipson, Elena S.

Quantifying the total effect of edge interventions in discrete multistate networks

• DOI: 10.1016/j.automatica.2020.109453
• 发表时间: 2021
• 期刊: Autom.
• 作者: D. Murrugarra;Elena S. Dimitrova