ATD: Next Generation Statistical Learning Theory and Methods for Multimodal Spatio-Temporal Data with Application to Computer Vision

该项目的主要目的是为新时代的时空数据开发下一代统计理论和机器学习方法，这些数据出现在基于技术的现代世界背景下，如计算机视觉，自动驾驶汽车和成像。传统的空间数据统计理论和建模的核心在于研究区域内的插值和预测。此外，由于许多强有力的假设，现有的技术是限制性的。除了时空数据建模的新方法外，该项目还考虑了空间对象的分类和预测。信息技术的快速发展使得以多种方式收集大量数据成为可能，这对数据科学家在真实的时间内多任务处理大量数据提出了严峻的挑战。传统的基于矢量的统计建模计算效率低，不足以在复杂和高维背景下的空间对象的分类。该项目提供了一个更广泛的和非标准的框架来处理这样大量的时空数据。所提出的理论和方法是基于低训练样本的计算机视觉应用。该项目将为本科生和研究生提供培训。该项目旨在提供两种创新的时空数据建模方法，人工神经网络和张量以及空间对象分类。这些技术在应用机器学习文献中得到了很好的建立，但与统计学中的传统时空分析不同。所提出的研究建立在使用机器学习技术捕获时空依赖性的基础上，以避免对大的协方差矩阵进行建模并捕获复杂的时空依赖性。该技术避免指定大的协方差矩阵，使模型的计算效率和依赖于较少的分布假设。这些方法的数学基础不仅发展了新的统计理论，而且还消除了由于缺乏足够的数学证明而导致的这些机器学习方法的价值损失。 该项目的另一个重要特点是，它考虑了通常具有低训练样本的计算机视觉应用。流行的机器学习技术，如深度网络，神经网络或高阶张量，需要大量的训练样本来构建有效的系统。 这个项目的一个主要目的是克服这个问题，采用几种降维技术，可以处理高维时空数据与小样本量，而不会过度拟合的模型。该项目将推进高维机器学习理论和方法的研究。该项目开发的理论和方法为处理大型复杂时空数据提供了一个通用框架，并在统计学、计算机科学、神经成像、机器学习和数据科学等多学科领域产生了广泛的影响。该奖项反映了NSF的法定使命，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。

The main purpose of this project is to develop next-generation statistical theory and methods of machine learning for new age spatio-temporal data that are arising in technology-based modern world contexts such as computer vision, self-driving cars, and imaging. The key focus of traditional statistical theory and modeling for spatial data lies mostly in interpolation and prediction within the study region. Further, the available techniques are restrictive because of many strong assumptions. Besides new ways of modeling spatio-temporal data, this project considers the classification and prediction of spatial objects. The rapid development of information technology is making it possible to collect massive amounts of data in multiple modalities, posing serious challenges to data scientists for multi-tasking the tremendous amount of data in real time. Conventional vector-based statistical modeling is computationally inefficient and inadequate for the classification of spatial objects in complex and high dimensional contexts. This project provides a broader and nonstandard framework for handling such massive spatio-temporal data. The proposed theory and methods are grounded with computer vision applications with low training sample. The project will provide training to undergraduate and graduate students. This project aims at providing two innovative ways of modeling spatio-temporal data, artificial neural networks, and tensor and classifying spatial objects. The techniques are well established in applied machine learning literature but distinguish themselves from the traditional spatio-temporal analysis in statistics. The proposed research builds upon capturing spatio-temporal dependence using machine learning techniques to avoid modeling large covariance matrix and capture complex spatio-temporal dependence. The techniques avoid specifying big covariance matrices to make the models computationally efficient and rely on less distributional assumptions. The proposed mathematical foundations for these methods not only develop new statistical theories, but also eliminate the value loss of these machine learning methods due to lack of adequate mathematical justifications. Another important feature of this project is that this considers computer vision applications which generally come with low training sample. The popular machine learning techniques such as deep net, neural net, or higher order tensors require large training sample for building effective systems. A major thrust of this project is to overcome this issue by adopting several dimension reduction techniques that can handle high-dimensional spatio-temporal data with small sample size without overfitting the model. The project will advance research in high dimensional machine learning theory and methods. The theory and methods developed in this project serve a general framework of dealing with large and complex spatio-temporal data and has broader impacts in multidisciplinary fields including statistics, computer science, neuroimaging, machine learning, and data science.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.