CAREER: Structured Learning of Distribution Spaces

公共领域和科学数据的数量和复杂性的快速增长带来了新的和令人兴奋的挑战。该项目旨在开发分布空间结构化学习的理论框架，以及识别和利用高维大容量数据中概率结构的研究工具。该项目位于多个学科的交叉点：信号处理，模式识别，机器学习，概率和统计，因此将促进这些学科之间的合作。将所提出的框架应用于数据驱动的医学诊断和生态研究，将进一步扩大该项目在计算数据分析领域之外的影响。此外，本研究设定了一个目标，以丰富本科生和研究生的教育质量，通过令人兴奋的研究，应用和新的course.The研究框架的整合几何约束的概率建模和高效的优化方法推理的多个实例数据。该项目提出了以下任务：i）多个离散概率模型的置信约束联合估计，ii）基于几何约束的最大熵模型的多个分布的联合学习，以及iii）将开发的框架直接应用于分析用于医疗诊断的临床流式细胞术数据和用于生态研究的原位生物声学数据。

A rapid acceleration in both volume and complexity of public domain and scientific data presents new and exciting challenges. This project aims to develop a theoretical framework for structured learning of distribution spaces and study tools for identifying and utilizing probabilistic structure in high-dimensional large volume data. This project lies within the intersection of multiple disciplines: signal processing, pattern recognition, machine learning, probability and statistics, and thus will foster collaboration among these disciplines. The application of the proposed framework to data-driven medical diagnosis and ecological research will further the impact of this project beyond the realm of computational data analysis. Additionally, this research sets a goal to enrich the quality of education for both undergraduate and graduate students, through exciting integration of research, application, and new curriculum.The research framework consists of geometrically-constrained probabilistic modeling and efficient optimization approaches for inference of multiple instance data. The project sets forth the following tasks i) confidence-constrained joint estimation of multiple discrete probability models, ii) joint learning of multiple distribution based geometrically-constrained maximum-entropy models, and iii) direct application of the developed framework to the analysis of clinical flow cytometry data for medical diagnosis and in-situ bioacoustics data for ecological research.