ATD: Landscape Networks and Nonlinear Diffusions for Anomaly Detection and Active Learning

统计和机器学习正在彻底改变科学领域，从计算机视觉到医学，再到自然语言处理和自然物理定律的推断。尽管有这些快速而令人印象深刻的经验进步，但机器学习在数学上仍然只有部分理解。特别是，无监督的异常检测，其中算法必须区分背景与异常，没有标记的数据和主动学习，其中只有一个非常小的，但仔细选择的数量的点可以查询标签是成熟的转型进步。随着传感器产生越来越多的数据集，庞大的数据量使人类无法生成传统监督学习算法所需的大型训练集。机器学习的未来依赖于开发新的数学方法来进行无监督和主动学习，其中不需要或只需要很少的训练数据。 这一方向的创新有可能改变计算医学、网络安全和图像处理等不同领域。 本研究计画将于第二、三年资助一位研究生，开发时空资料异常侦测与主动学习之新演算法。重点是分析高维，时间演变的数据集的方式，是强大的非线性几何形状，可变的采样率，大量的噪声和离群值。 PI提出了两个不同但相关的研究方向。首先，设计使用景观聚类网络的多时相异常检测算法。这种方法处理随时间变化的分布和标签集群和异常在不同级别的粒度，提供置信度估计和不确定性量化。其次，将开发用于时空数据的扩散几何主动学习算法，以允许人类分析师从算法中标记少量查询。这些查询是经过精心选择的，人类分析师提供的标签可以以最小的计算负担从根本上提高聚类和异常检测。所提出的方法是强大的复杂的数据几何形状，时间采样率，噪声和离群值，和环境的数据维数。除了机器学习的主题之外，该项目还对概率论、调和分析、谱图理论、高维统计和计算线性代数做出了更广泛的贡献。 数学和算法的贡献将与分析大型时空数据集的科学合作并行发展。该项目的重点是异常检测和主动学习在三个不同的时空数据设置：大规模通勤网络，高光谱图像分析，高能粒子物理。所提出的方法允许实时异常和威胁检测，是可扩展的，并减轻了对大型训练集的需求。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Statistical and machine learning are revolutionizing scientific fields ranging from computer vision, to medicine, to natural language processing, and inference of natural physical laws. Despite these rapid and impressive empirical advances, machine learning remains only partially understood mathematically. In particular, unsupervised anomaly detection in which algorithms must distinguish background from anomaly with no labeled data and active learning in which only a very small but carefully selected number of points may be queried for labels are ripe for transformational advances. As sensors generate ever increasing datasets, the sheer volume of data overwhelms human capacity for generating the kinds of large training sets necessary for traditional supervised learning algorithms. The future of machine learning relies on developing new mathematical approaches to unsupervised and active learning, where no or little training data is required. Innovations in this direction have potential to transform fields as diverse as computational medicine, network security, and image processing. This project will support 1 graduate student in the second and third years of the grant.This research project develops new algorithms for anomaly detection and active learning in spatiotemporal data. The emphasis is on the analysis of high-dimensional, time-evolving data sets in a manner that is robust to nonlinear geometries, variable sampling rates, and large quantities of noise and outliers. The PI proposes two distinct but related lines of research. First, to devise multitemporal anomaly detection algorithms using landscape cluster networks. This approach handles temporally varying distributions and labels clusters and anomalies at different levels of granularity, providing confidence estimates and uncertainty quantifications. Second, diffusion geometric active learning algorithms for spatiotemporal data will be developed to allow a human analyst to label a small number of queries from the algorithm. These queries are carefully chosen, and the labels provided by the human analyst can radically improve cluster and anomaly detection at minimal computational burden. The proposed methods are robust to complicated data geometries, temporal sampling rates, noise and outliers, and ambient dimensionality of the data. Beyond the topics of machine learning, this project makes broader contributions to probability theory, harmonic analysis, spectral graph theory, high-dimensional statistics, and computational linear algebra. Mathematical and algorithmic contributions will be developed in parallel with scientific collaborations analyzing large spatiotemporal datasets. This project focuses on anomaly detection and active learning in three distinct spatiotemporal data settings: large-scale commuting networks, hyperspectral image analysis, and high energy particle physics. The proposed methods allow for real-time anomaly and threat detection, are scalable, and mitigate the need for large training sets.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.