III: Small: Nonparametric Structure Learning for Complex Scientific Datasets

该项目汇集了来自约翰·霍普金斯大学、卡内基梅隆大学和芝加哥大学的跨学科研究团队，以开发从复杂的科学数据集中发现隐藏结构的方法、理论和算法，而不需要做出强有力的先验假设。结果包括实用的模型和被证明是正确的算法，可以帮助科学家进行复杂的数据分析。该项目的应用领域包括基因组学、认知神经科学、气候科学、天体物理学和语言处理。该项目有五个目标：(I)高维非参数结构学习：在标准结构学习问题中，可以对随机向量X进行观测，目标是估计X的分布的结构。当维度较大时，非参数结构学习变得具有挑战性。该项目开发了新的方法，并为这一问题建立了理论保证；(Ii)非参数条件结构学习：在许多应用中，有兴趣估计一个高维随机向量X的结构，条件是另一个随机向量Z。正在开发估计给定Z的X的结构的非参数方法，建立在研究人员开发的图值和流形值回归的最新方法的基础上；(Iii)正则化参数选择：大多数结构学习算法至少有一个调整参数来控制偏差-方差权衡。传统的参数选择方法不适用于复杂的非参数结构学习问题。该项目探索了基于稳定性的正则化选择方法；(Iv)并行和在线非参数学习：处理大规模数据是许多非参数方法的瓶颈。该项目开发了并行和在线技术，以将非参数学习算法扩展到大规模问题；(V)用于非参数结构学习问题的极小极大理论：极小极大理论表征了学习算法的性能极限。对于复杂的高维非参数结构学习，鲜有理论结果为人所知。该项目在这种背景下发展了新的极小极大理论。该项目的成果将通过在科学期刊和主要会议上的出版物以及实现这项研究的非参数结构学习算法的软件的免费传播来传播。该项目的更广泛的影响包括：为广泛的科学家和工程师创建强大的数据分析技术和软件，以分析和理解更复杂的科学数据；加强多机构(约翰·霍普金斯大学、卡内基梅隆大学和芝加哥大学)的研究人员之间的合作和跨学科互动；以及在不同的科学界广泛传播这项研究的结果。有关该项目的更多信息，请访问：http://www.cs.jhu.edu/~hanliu/nsf116730.html.

The project brings together an interdisciplinary team of researchers from Johns Hopkins University, Carnegie Mellon University, and the University of Chicago to develop methods, theory and algorithms for discovering hidden structure from complex scientific datasets, without making strong a priori assumptions. The outcomes include practical models and provably correct algorithms that can help scientists to conduct sophisticated data analysis. The application areas include genomics, cognitive neuroscience, climate science, astrophysics, and language processing.The project has five aims: (i) Nonparametric structure learning in high dimensions: In a standard structure learning problem, observations of a random vector X are available and the goal is to estimate the structure of the distribution of X. When the dimension is large, nonparametric structure learning becomes challenging. The project develops new methods and establishes theoretical guarantees for this problem; (ii) Nonparametric conditional structure learning: In many applications, it is of interest to estimate the structure of a high-dimensional random vector X conditional on another random vector Z . Nonparametric methods for estimating the structure of X given Z are being developed, building on recent approaches to graph-valued and manifold-valued regression developed by the investigators; (iii) Regularization parameter selection: Most structure learning algorithms have at least one tuning parameter that controls the bias-variance tradeoff. Classical methods for selecting tuning parameters are not suitable for complex nonparametric structure learning problems. The project explores stability-based approaches for regularization selection; (iv) Parallel and online nonparametric learning: Handling large-scale data is a bottleneck of many nonparametric methods. The project develops parallel and online techniques to extend nonparametric learning algorithms to large scale problems; (v) Minimax theory for nonparametric structure learning problems: Minimax theory characterizes the performance limits for learning algorithms. Few theoretical results are known for complex, high-dimensional nonparametric structure learning. The project develops new minimax theory in this setting. The results of this project will be disseminated through publications in scientific journals and major conferences, and free dissemination of software that implements the nonparametric structure learning algorithms resulting from this research.The broader impacts of the project include: Creation of powerful data analysis techniques and software to a wide range of scientists and engineers to analyze and understand more complex scientific data; Increased collaboration and interdisciplinary interactions between researchers at multiple institutions (Johns Hopkins University, Carnegie Mellon University, and the University of Chicago); and Broad dissemination of the results of this research in different scientific communities. Additional information about the project can be found at: http://www.cs.jhu.edu/~hanliu/nsf116730.html.