Collaborative Research: Selection Methods for Algebraic Design of Experiments

数据科学已经成为一个重要的领域，可以根据从医疗保健和住房等不同行业收集的数据做出决策。 尽管有了手机应用程序、商家会员卡和社交媒体账户，数据已经很丰富了，但更多的数据是否能转化为更多的知识仍然是个问题。此外，数据的收集和储存可能存在问题，特别是在数据敏感的情况下，临床试验和遗传实验往往就是这种情况。 选择信息丰富的数据对于创建能够可靠预测未来实验结果的模型至关重要。关于所需数据量的结果很少，目前还没有生成明确识别预测模型的特定数据集的指导方针。作为发展完整理论的第一步，PI将专注于由有限值非线性多项式函数描述的模型。(For例如，WedMD的症状查询中的内部“函数”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多项式模型的最小数据集，并研究这些数据集的属性。 从这些计算实验中，他们将建立适当的理论，设计算法，并生成代码，这些代码可以在以后开发成具有图形用户界面的软件。研究生将在项目的每个组成部分的适当水平参与。这样的经历将为他们提供可能的MS或博士论文主题，并很可能激发他们在STEM学科的职业生涯。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设计，网络推理和有限动力系统领域。这些算法将作为实验者确定识别感兴趣网络结构所需数据的指南。这些知识有可能大幅减少因数据太多而信息太少而造成的资源浪费。虽然这是一个大数据时代，但更多的数据是否会转化为更多的知识仍然是一个问题。特别是当收集数据是昂贵的或耗时的，因为它通常是临床试验和生物分子实验的情况下，选择信息丰富的数据的问题变得至关重要的创建相关的模型。布尔状态多元多项式函数已成功地用于从离散数据对复杂网络进行建模;然而，很少有关于此类模型所需数据量的结果，大多数仅适用于布尔模型。仍然不知道哪些数据点明确地识别这样的离散模型，并且因此，没有用于生成将明确地识别模型的特定数据集的方法。 PI将通过开发适当的理论、设计算法和生成稍后可以内置到软件中的代码来解决数据的最小性和特异性问题，以唯一地识别离散多项式模型。研究生将在项目的每个组成部分的适当水平参与。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时出现的计算伪影的影响来改进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地识别模型，从而推进实验设计和网络推理领域。所提出的工作还将通过建立用于唯一模型识别的最小数据量来增加多项式动力系统作为复杂网络模型的实用性。这些算法将作为实验者确定识别感兴趣网络结构所需数据的指南。这种知识有可能大大减少实验的数量，并消除产生的数据几乎没有内在价值。

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.