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

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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.