Multiscale data geometric networks for learning representations and dynamics of biological systems

近年来，单细胞测序技术产生了大量高通量、高维的生物医学数据。此外，与过去的此类数据相比，目前的做法涉及收集多个单细胞数据集（例如，针对大型队列中的每个患者），这些数据集可以表示随时间或不同条件下的数据，并且可以作为点云进行计算分析。我们非常需要新的数学和机器学习技术来处理这些类型的复杂数据，从而获得有关健康和疾病过程的有意义和预测性的见解。虽然生物医学领域使用的大多数机器学习技术都是由语言或视觉（图像）模型引起的监督技术，但该项目侧重于开发更复杂数据结构的多尺度几何和拓扑表示。这样的表示使我们能够结合数据科学前沿的几个领域的进展，包括几何深度学习，流形学习和谐波分析，以便以可解释的方式分析和预测这些数据。该研究将包括几个生物医学应用，如表征COVID-19的免疫反应，追踪转移性癌症的进展，预测免疫治疗的有效性，以及了解分化。此外，这些方法所解决的挑战将使在不同实验环境中收集复杂高通量数据的广泛领域取得新进展。该项目将提供表征学习技术，以探索和展示高维和复杂的数据类型，包括点云，在各种条件下收集的图，以执行机器学习任务。推力1将涉及数据几何特征的发展，以表征点云数据，在此基础上，将创建一类新的神经网络，用于回归来自各种系统的单细胞数据。推力2将侧重于通过构造非对称核并使用这些核进行嵌入、推理和特征预测来保存有向信息的方法。这将导致有向图神经网络的创建，利用在点云数据的有向图拉普拉斯上定义的几何散射。这将用于学习和处理来自基因调控和代谢网络的数据。推力3将重点关注使用最佳传输正则化神经ode和pde从静态快照单细胞数据推断连续动态插值的动力学，并产生潜在生成模型的解释。此外，它将涉及使用数据几何和拓扑来预测和分类动态定量表示，并将在上皮细胞的癌症和钙信号数据上进行验证。这里开发的技术将在使用神经网络来表示和预测点云数据方面提供根本性的进步，并提供新的方法来解决跟踪动态生物过程的问题。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。

Recent years have seen significant volumes of high throughput, high dimensional, biomedical data arising from single cell sequencing technologies. Further, in contrast to past data of this type, current practices involve the collection of multiple single cell datasets (e.g., for each patient in a large cohort), which can represent data over time or in different conditions and can be analyzed computationally as point clouds. There is a great need for new mathematical and machine learning techniques to be able to process these types of complex data to gain meaningful and predictive insight on healthy and disease processes. While the majority of machine learning techniques used in the biomedical domain have been supervised techniques arising from language or vision (image) models, this project focuses on developing multiscale geometric and topological representations of more complex data structures. Such representations allow us to combine advances in several fields at the forefront of data science, including geometric deep learning, manifold learning, and harmonic analysis in order to analyze and predict from this data in an interpretable way. The research will include several biomedical applications, such as characterizing immune response in COVID-19, tracking the progress of metastatic cancer, predicting the effectiveness of immunotherapy, and understanding differentiation. Furthermore, the challenges addressed by these methods will enable new advances in a wide range of fields where complex high throughput data is collected in varying experimental environments. The project will provide representation learning techniques to explore and featurize high dimensional and complex datatypes including point clouds, graphs collected in a variety of conditions in order to perform machine learning tasks. Thrust 1 will involve the development of data geometric features to characterize point cloud data, based on which a novel class of neural networks will be created for regression on single cell data from a variety of systems. Thrust 2 will focus on methods for preserving directed information, by constructing asymmetric kernels and using these kernels for embedding, inference, and feature prediction. This will lead to the creation of directed graph neural networks that utilize geometric scattering as defined on a directional graph Laplacian of point cloud data. This will be used to learn and process data from gene regulatory and metabolic networks. Thrust 3 will focus here on inferring dynamics for interpolation of continuous dynamics from static snapshot single cell data using optimal transport-regularized neural ODEs and PDEs and producing interpretations of the underlying generative models. Further, it will involve representing dynamics quantitatively using data geometry and topology for prediction and classification, and will be validated on cancer and calcium signaling data from epithelial cells. The techniques developed here will provide fundamental advances in the use of neural networks to represent and make predictions on point cloud data, as well as enable new ways to tackle the problem of tracking dynamic biological processes over them.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.