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

数据驱动设计正在许多广泛使用的系统中带来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成像的医疗诊断中找到，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，大量使用不太了解的数据可能会造成重大风险。例如，数据可能会引入对特定系统输出的偏差（例如，导致不正确的诊断）或性能可能在数据收集中甚至很小的变化下显著降低（例如，麦克风特性、相机分辨率）。这些风险是更广泛采用数据驱动工具的主要障碍，特别是在关键应用程序中。 该项目开发的方法来选择数据，以改进系统设计，基于大规模数据集的新模型。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。在许多应用中，例如传感、异常检测、分类、识别或识别，系统的设计是通过首先收集大量数据，然后使用该数据优化系统参数。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个主要挑战，估计通常基于训练集上的端到端性能。这些任务的例子包括（i）估计系统精度，（ii）表征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）预测它们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。这项研究的重点是理论，算法和实际方面的系统表征和设计。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形的问题，开发渐近结果，将数据的分布与图形和相关图形信号的属性联系起来。在算法方面，开发了用于图构建和任务复杂度估计的有效方法，目标是选择最具代表性的数据集。作为一个应用程序，考虑了实用的深度学习架构，研究了提高其鲁棒性的方法，并开发了主动学习和迁移学习的新策略。该奖项反映了NSF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.