CIF: Small: Graph Signal Processing Methods for Data-driven System Design

在许多广泛使用的系统中，数据驱动设计正在导致前所未有的性能改进。最近成功的例子可以在语音识别、高级视频分析或基于图像的医学诊断中找到，仅举几例。这个项目的动机是观察到更多的数据并不总是导致更好的系统设计。事实上，一旦部署系统，大量使用理解不佳的数据可能会产生重大风险。例如，数据可能会引入对特定系统输出的偏差（例如，导致错误的诊断），或者即使数据收集的微小变化（例如，麦克风特性，相机分辨率）也可能显著降低性能。这些风险是广泛采用数据驱动工具的主要障碍，特别是在关键应用中。本项目基于大规模数据集的新模型，开发了为改进系统设计选择数据的方法。该项目的最终目标是通过基于最具代表性的数据集而不是简单地使用最大的数据集来设计系统，从而降低部署风险。在传感、异常检测、分类、识别或识别等许多应用中，系统的设计首先要收集大量数据，然后利用这些数据优化系统参数。随着任务复杂性、数据大小和系统参数数量的增加，系统分析和表征任务成为一项主要挑战，其估计通常基于训练集的端到端性能。这些任务的例子包括(i)估计系统的准确性，（ii）描述系统对数据变化的稳定性，（iii）确定训练所需的正确数据量，或（iv）预测其推广到不同情况的能力。在这个项目中，开发了基于图的方法来描述高维空间中的大型数据集。本研究的重点是系统表征和设计的理论、算法和实践方面。在理论方面，该项目解决了设计捕获数据空间相关属性的图的问题，开发了将数据分布与图和相关图信号的属性联系起来的渐近结果。在算法方面，开发了高效的图构建和任务复杂性估计方法，目标是能够选择最具代表性的数据集。作为一种应用，考虑了实际的深度学习架构，研究了增强其鲁棒性的方法，并开发了主动学习和迁移学习的新策略。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。

Data-driven design is leading to unprecedented performance improvements in many widely used systems. Examples of recent successes can be found in speech recognition, advanced video analysis or imaging-based medical diagnosis, to name just a few. This project is motivated by the observation that more data does not always lead to better system design. In fact, extensive use of poorly understood data can create significant risks once systems are deployed. For example, data may introduce bias toward specific system outputs (e.g., lead to incorrect diagnoses) or performance might degrade significantly under even small changes in data collection (e.g., microphone characteristics, camera resolution). These risks are a major obstacle to wider adoption of data-driven tools, in particular in critical applications. This project develops methods to select data for improved system design, based on new models for large scale datasets. The ultimate goal of the project is to reduce deployment risk by designing systems based on the most representative dataset rather simply using the largest dataset. In many applications, such as sensing, anomaly detection, classification, recognition or identification, systems are designed by first collecting significant amounts of data, and then optimizing system parameters using that data. As task complexity, data size and the number of system parameters increase, system analysis and characterization tasks become a major challenge, with estimates often based on end-to-end performance on the training set. Examples of these tasks include (i) estimating system accuracy, (ii) characterizing system stability to changes in data, (iii) determining the correct amounts of data needed for training or (iv) predicting their ability to generalize to different situations. In this project, graph-based approaches are developed to characterize large datasets in high dimensional space. This research is focused on theoretical, algorithmic and practical aspects of system characterization and design. On the theoretical front, this project tackles the problem of designing graphs that capture relevant properties of the data space, developing asymptotic results to link the distribution of the data to properties of graphs and related graph signals. On the algorithmic front, efficient methods for graph construction and task complexity estimation are developed, with the goal of enabling selection of the most representative dataset. As an application, practical deep learning architectures are considered, methods to increase their robustness are studied, and new strategies for active and transfer learning are developed.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.