Structural Learning and Statistical Inference for Large-Scale Data

该项目旨在开发新的结构学习和统计推理程序，以获取大规模数据的一些基本结构，这些结构来自遗传学、生物学、神经科学、金融和气象学等科学研究。将开发新的随机建模、计算算法和统计推理工具，应用于神经科学研究中的多通道脑电信号记录、多对象功能磁共振成像和多神经元棘波训练，以及识别气候数据的结构变化和遗传学中的拷贝数变化。这项研究的结果将帮助科学家有效地分析大规模的成像、时间和空间数据，从而通过它们对科学、公共卫生和信息技术的这些应用的直接影响，对我们的社会产生更广泛的影响。这些进展的传播将促进新的知识发现，并加强跨学科合作。这项研究还将与教育实践相结合，设计关于分析复杂数据的新统计方法的常规、研讨会或短期课程，并有利于本科生、研究生和代表性不足的少数民族的培训和学习。这项研究工作侧重于从根本上不同类型的结构的统计学习，最终目标是更好地理解复杂系统。项目1将学习大型泊松网络中的有向无环图结构，其动机是从集合神经棘波训练数据推断神经连接，以广泛的多变量点过程数据为基础。相关的概率机制将为理解与挖掘神经元之间因果关系相关的图参数的估计器的统计性质提供新的见解。受多通道脑电记录的特征提取和源分离以及非线性时间信号处理的启发，项目2将开发一类结构成分分析(SCA)的非线性非光滑组合，以从观察到的混合信号中提取隐藏成分信号。开发的SCA将在科学研究中得到更广泛的应用。基于识别和理解气候趋势的结构性变化，以及与遗传疾病相关的基因拷贝数的结构性变化，项目3将开发一种新的两步自适应跳跃检测程序，用于同时选择未知数量的跳跃点并在灵活的非参数回归模型中检测它们的位置。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims at developing new structure learning and statistical inference procedures for capturing some essential structures of large-scale data, emerging from scientific studies in genetics, biology, neuroscience, finance, and meteorology, among others. New tools for stochastic modeling, computational algorithms, and statistical inference applied to multi-channel brain EEG recordings, multi-subject fMRI and multiple neuron spike trains in neuroscience research, and identifying structural changes in climate data and copy number variation in genetics, will be developed. Outcomes of this study will help scientists to efficiently analyze large-scale imaging, temporal and spatial data, and thus will have broader impacts on our society through their direct impacts on these applications to science, public health, and information technology. Dissemination of these developments will enhance new knowledge discoveries, and strengthen interdisciplinary collaborations. The research will also be integrated with educational practice through designing either regular, seminar or short courses on new statistical approaches for analyzing complex data as well as benefitting the training and learning of undergraduate, graduate students and underrepresented minorities.This research work focuses on statistical learning of fundamentally distinct types of structures, with the ultimate goal of better understanding of complex systems. Motivated from inferring neural connectivity from the ensemble neural spike train data, Project 1 will learn the directed acyclic graph structure in a large Poisson network, underlying a wide array of multivariate point process data. The related probabilistic mechanism will provide new insights into understanding statistical properties of the estimators for graph parameters relevant to mining the causal relation among neurons. Inspired by feature extraction and source separation from multi-channel brain EEG recordings and non-linear temporal signal processing, Project 2 will develop a class of non-linear non-smooth combinations of structured component analysis (SCA) to extract hidden component signals from observed mixed signals. The SCA developed will be more broadly applicable in scientific studies. Motivated from identifying and understanding structural changes in climate trends, and structural variation in gene copy numbers associated with genetic diseases, Project 3 will develop a novel two-step adaptive procedure of jump detection, for simultaneously selecting the unknown number of jump points and detecting their locations in the flexible non-parametric regression model.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.