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的高通量、高维、生物医学数据。此外，与过去这种类型的数据相比，当前的做法涉及收集多个单细胞数据集(例如，对于大队列中的每个患者)，其可以表示随时间或在不同条件下的数据，并且可以通过计算分析为点云。迫切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，以获得对健康和疾病过程的有意义和预测性的洞察。虽然生物医学领域中使用的大多数机器学习技术都是源于语言或视觉(图像)模型的有监督技术，但该项目专注于开发更复杂数据结构的多尺度几何和拓扑表示。这样的表示允许我们结合数据科学前沿的几个领域的进展，包括几何深度学习、流形学习和调和分析，以便以可解释的方式分析和预测这些数据。这项研究将包括几个生物医学应用，例如表征新冠肺炎的免疫反应，跟踪转移癌症的进展，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的实验环境中收集复杂的高通量数据的广泛领域取得新的进展。该项目将提供表示学习技术，以探索高维和复杂的数据类型并将其具体化，包括在各种条件下收集的点云、图表，以便执行机器学习任务。推力1将涉及开发数据几何特征来表征点云数据，在此基础上将创建一类新的神经网络，用于对来自各种系统的单细胞数据进行回归。推力2将专注于通过构造非对称核并将这些核用于嵌入、推理和特征预测来保存有向信息的方法。这将导致创建有向图神经网络，该有向图神经网络利用在点云数据的有向图拉普拉斯上定义的几何散射。这将被用来学习和处理来自基因调控和代谢网络的数据。这里，推力3将侧重于利用最优传输正则化神经常微分方程组和偏微分方程组，从静态快照单细胞数据推断连续动态内插的动态，并产生对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定量表示动力学以进行预测和分类，并将在来自上皮细胞的癌症和钙信号数据上得到验证。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，并使新的方法能够解决跟踪点云数据上的动态生物过程的问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.