CAREER: New Representations of Probability Distributions to Improve Machine Learning --- A Unified Kernel Embedding Framework for Distributions

计算智能与我们的日常生活息息相关。网络搜索、天气预报、检测金融欺诈、医疗和教育都受益于这种无处不在的技术。计算智能中的问题，如图像分类和预测新材料的性能，产生了大量的高维、复杂的数据。计算智能中的许多算法依赖于概率分布，而这样的数据可以携带不寻常的分布，挑战传统的建模方法。(例如，它们通常不是教科书上的分布，如高斯分布。)在某些应用中，输入到算法的数据本身就是概率分布。现有的技术既无法捕捉不寻常的分布，又无法在不停止计算的情况下扩展到数百万个数据点。迫切需要一个灵活、高效的框架来表示、学习和推理由这些问题产生的数据集。这个项目将通过开发一个新颖和统一的框架来表示、建模、学习和使用计算智能中的概率分布来解决这些挑战。为了评估新技术的实用性，该项目将在计算机图像分析、材料科学和流式细胞术(一种用于细胞计数、细胞分类和蛋白质工程的生物技术技术)等现实世界的困难问题上对它们进行测试。该项目是美国国家科学基金会的职业奖项，将把研究成果与几个教育创新项目相结合。新课程将面向本科生和研究生，重点关注代表不足群体的学生。一门新的在线课程将被创建，以使大量在线硕士学生能够访问结果。最后，高级高中数学教师将设计与该研究相关的问题，用于高级高中学生的数学竞赛。该项目将(1)为分布数据和具有细粒度统计特性的分布创建一个新颖而统一的非参数核框架，(2)开发用于大数据非参数分析的原则性和可扩展性算法。统一的核嵌入框架将极大地推动大规模非参数数据分析，并在连接数据分析中传统上分离的研究领域方面发挥重要的协同作用，包括核方法、图形模型、优化、非参数贝叶斯方法、泛函分析和张量数据分析。除了算法方法的进步，在大规模图像分类、流式细胞仪和材料性能预测方面的应用也有可能对社会产生革命性的影响。

Computational intelligence touches our lives daily. Web searches, weather prediction, detecting financial fraud, medicine and education benefit from this ubiquitous technology. Problems in computational intelligence such as image classification and predicting properties of new materials produce copious amounts of high-dimensional, complex data. Many algorithms in computational intelligence rely on probability distributions, and such data can carry unusual distributions that challenge traditional methods of modeling. (For example, they are typically not textbook distributions such as the Gaussian.) In some applications, the data input to the algorithms are themselves probability distributions. Existing techniques are cannot both capture unusual distributions and scale to millions of data points without stalling the computation. There is a pressing need for a flexible, efficient framework for representing, learning, and reasoning about datasets arising from these problems.This project will address these challenges by developing a novel and unified framework to represent and model, learn, and use probability distributions in computational intelligence. To evaluate the utility of the new techniques, the project will test them on difficult real-world problems in computer image analysis, materials science, and flow cytometry (a biotechnology technique used for cell counting, cell sorting, and protein engineering).The project, an NSF CAREER award, will integrate the research results with several education intiatives. New curricula will be designed for both undergraduate and graduate students, with empahsis on students from under-represented groups. A new online course will be created to make the results accessible to massive online masters students. Finally, advanced high school math teachers will be engaged to design problems related to the reserach for use in a math competition for advanced high school students.This project will (1) create a novel and unified nonparametric kernel framework for distributional data and distributions with fine-grained statistical properties, and (2) develop principled and scalable algorithms for nonparametric analysis of big data. The unified kernel embedding framework will advance large scale nonparametric data analysis significantly, and play an important synergistic role in bridging together traditionally separate research areas in data analysis, including kernel methods, graphical models, optimization, nonparametric Bayesian methods, functional analysis and tensor data analysis. In addition to advances in algorithmic methods, the applications to large-scale image classification, flow cytometry, and materials property prediction have the potential for transformative impact on society.