Collaborative Research: Data selection for unique model identification

虽然现在是大数据时代，但更多的数据是否会转化为更多的知识，这仍然是一个问题。特别是当生成数据昂贵或耗时时，就像临床试验和生物分子实验经常出现的情况一样，识别信息丰富的数据的问题对于创建能够可靠地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很少发表，目前还没有方法生成能够明确识别预测模型的特定数据集。这个研究项目涉及数据选择中的基本数学和计算问题。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和网络推理领域。正在开发的算法将作为实验学家确定识别感兴趣的网络结构所需的数据的指南。这种知识有可能大大减少由于数据太多而信息太少而造成的资源浪费。研究生将以适当的水平参与项目的每个组成部分。这样的经历将为硕士或博士学位论文提供可能的主题，并很可能激发参与者在STEM学科的长期职业参与。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。有限状态多元多项式函数已被成功地用于从离散数据中建立复杂网络模型；然而，关于这些模型所需的数据量的结果很少，大多数只适用于布尔模型。pi将通过发展适当的理论，实现理论结果作为算法，并将算法应用于重要的物理系统，解决数据的最小化和特异性问题，以唯一地识别离散多项式模型。所提出的工作还将增加多项式动力系统作为复杂网络模型的效用，通过建立最少量的数据来进行唯一模型识别。

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.