Collaborative Research: Data selection for unique model identification

虽然现在是大数据时代，但仍然存在更多数据是否能转化为更多知识的问题。特别是当生成数据昂贵或耗时时（临床试验和生物分子实验经常出现这种情况），识别信息丰富的数据的问题对于创建能够可靠预测未来实验结果的模型至关重要。关于必要数据量的结果几乎没有发表，而且目前还没有方法来生成可以明确识别预测模型的特定数据集。该研究项目解决数据选择中的基本数学和计算问题。 通过确定选择数据集以唯一识别模型的标准，理论结果将推动实验设计和网络推理领域的发展。正在开发的算法将作为实验者确定识别感兴趣网络结构所需的数据的指南。这些知识有可能大大减少因数据过多而信息过少而造成的资源浪费。研究生将以适当的水平参与该项目的每个组成部分。这样的经历将为硕士提供可能的主题。或博士学位论文，很可能会激发参与者在整个职业生涯中参与 STEM 学科。作为开发完整理论的第一步，PI 将重点关注由有限值非线性多项式函数描述的模型。有限状态多元多项式函数已成功用于根据离散数据对复杂网络进行建模；然而，关于此类模型所需数据量的结果很少，其中大多数仅适用于布尔模型。 PI 将解决数据的最小性和特异性问题，通过开发适当的理论、将理论结果实现为算法并将算法应用于重要的物理系统来唯一地识别离散多项式模型。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提高多项式动力系统作为复杂网络模型的实用性。

While this is the age of big data, there is still a question of whether more data translates to more knowledge. Particularly when generating data is expensive or time consuming, as it is often the case with clinical trials and biomolecular experiments, the problem of identifying 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 methods for generating specific data sets which would unambiguously identify a predictive model. This research project addresses fundamental mathematical and computational questions in data selection. The theoretical results will advance the fields of design of experiments and network inference through the determination of criteria for selecting data sets to uniquely identify models. The algorithms under development 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. Graduate students will participate at the appropriate level in each component of the project. Such an experience will provide possible topics for M.S. or Ph.D. dissertations and will very likely inspire career-long involvement of the participants in the STEM disciplines.As a first step towards developing a complete theory, the PIs will focus on models described by finite-valued nonlinear polynomial functions. 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. The PIs will address the issue of the minimality and specificity of data to uniquely identify discrete polynomial models by developing the appropriate theory, implementing the theoretical results as algorithms, and applying the algorithms to important physical systems. 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.