Collaborative Research: CDS&E: Scalable Inference for Spatio-Temporal Markov Random Fields

现代系统被认为是大规模的，具有复杂、动态和未知拓扑的层次结构。例如，在基因组学中，基因之间的相互作用可以通过跨不同细胞的时空基因调控网络来建模。对时间和空间上重新连接的基因表达网络的推断对动态疾病过程具有巨大的影响，为相互作用的生物过程在空间和时间上的动态变化提供了关键的机制见解。这种相互连接的系统的行为可以通过时空图形模型来捕获。现有的推断这些模型的方法存在一些统计和计算上的缺陷，这使得它们在现实环境中不切实际。为了弥合这一知识差距，该项目旨在开发有效的计算工具，用于时空图形模型的推理，这些模型不仅是可证明的最佳的，而且是自适应的，可并行的，并且可以在有意义的规模上实现。在本建议中开发的方法将在推断肿瘤发生的基因网络的背景下进行研究。通过这些努力产生的数据集将伴随着发达的分析工具，以获得对生物过程背后的基因网络本质的机械见解。更广泛地说，提议的机器将产生可由领域专家解释的模型，并将产生一组丰富的公开可用数据集，可用作不同推理方法的测试平台，从而产生更广泛的人工智能(AI)-人类合作。在图形模型推理方面的许多进展都是基于放宽正则化的最大似然估计（MLE），这既不能产生理想的统计特性，也不能与时空设置中遇到的维度相匹配。该项目将通过脱离正则化的MLE范式，并诉诸于一类新的具有组合性质的约束优化问题来解决这些挑战，这些问题可以系统地捕获时空图形模型的隐藏但有用的结构。由于基于mle的方法过于复杂，它们的实际实现不能同时保证计算效率和良好的统计性能。因此，所提出的方法将是第一个能够以统一的方式实现两全其美的系统推理框架。这类新的估计方法将对统计学习产生深远的影响：它将导致人们对可处理离散方法及其统计特性的使用重新产生兴趣，并将为发现适合于大维度和时空设置的新推理方法铺平道路。此外，拟议的项目将是第一个系统研究一类离散优化问题，这些问题目前知之甚少，因此也有助于组合和混合整数社区。鉴于其跨学科性质，该项目也将在很大程度上有助于培养未来几代数据科学研究人员。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modern systems are known to be massive-scale, with a hierarchy of complex, dynamic, and unknown topologies. For example, in genomics, the interactions among genes can be modeled via spatio-temporal gene regulatory networks across different cells. The inference of temporal and spatially-rewired gene expression networks carries enormous implications for dynamic disease processes, offering key mechanistic insights into the dynamic variations of interacting biological processes in space and time. The behavior of such interconnected systems can be captured via spatio-temporal graphical models. The existing methods for inferring these models suffer from several statistical and computational drawbacks which render them impractical in realistic settings. With the goal of bridging this knowledge gap, this project aims at developing efficient computational tools for the inference of spatio-temporal graphical models that are not only provably optimal, but also adaptive, parallelizable, and implementable in meaningful scales. The methods developed in this proposal will be studied in the context of inferring gene networks underlying oncogenesis. The datasets generated through these efforts will be accompanied with well-developed analytics tools to derive mechanistic insights into the nature of gene-networks underlying biological processes. More broadly, the proposed machinery will give rise to models that are interpretable by domain experts, and will lead to a rich set of publicly-available datasets that can be used as test-bed for different inference methods, resulting in broader artificial intelligence (AI)-human collaborations.Much of the progress in the inference of graphical models is based on the maximum likelihood estimation (MLE) with relaxed regularization, which neither result in ideal statistical properties nor scale to dimensions encountered in spatio-temporal settings. This project will address these challenges by departing from the regularized MLE paradigm, and resorting to a new class of constrained optimization problems with combinatorial nature that can systematically capture the hidden-but-useful structure of the spatio-temporal graphical models. Due to the prohibitively complex nature of the MLE-based methods, their practical implementations cannot simultaneously guarantee computational efficiency and favorable statistical performance. Therefore, the proposed approach will be the first systematic inference framework that can achieve the best of both worlds in a unified fashion. The new class of estimation methods will have a profound impact in statistical learning: it will lead to a renewed interest in the use of tractable discrete approaches and their statistical properties, and will pave the way towards the discovery of new inference methods suitable for the large-dimensional and spatio-temporal settings. In addition, the proposed project will be the first systematic study of a class of discrete optimization problems that are currently poorly understood, thus contributing to the combinatorial and mixed-integer communities as well. Given its interdisciplinary nature, the project will also largely contribute to training of future generations of researchers in data science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.