High-Dimensional Point Process Modeling with Applications to Large-scale Neuronal Activity Analysis

大规模点过程数据在各种科学和商业应用中无处不在，例如在神经科学中。该项目旨在开发一系列新的统计方法和机器学习算法，用于高维点过程数据的建模。这些方法可用于分析复杂的整体神经元活动数据，这是神经科学中理解神经元群的感觉编码、运动输出和认知功能机制的关键兴趣。这些方法也将有助于解决其他重要的科学问题，如预测地震的发生，捕捉星系的空间格局，表征社会网络，建模营销预测和供应链。该项目将促进来自不同领域的数据和领域科学家之间的跨学科合作，包括神经科学、环境科学、商业、流行病学、天文学、生态学和政治学。该项目将把研究与各级学生的教学和培训结合起来。用编程语言R和Python实现的软件包将被开发和分发以供广泛使用。分析多变量神经元尖峰序列数据带来了重大挑战，需要新的复杂工具来建模高维点过程。本项目旨在通过利用先进的张量分解技术，开发一个通用的多变量点过程回归模型，该模型允许高维点过程型响应和预测器。该方法将使研究人员能够对大量神经元进行联合建模，同时大大降低了模型维数，从而将数据高维的劣势转化为优势。该项目还将把额外的结构，如稀疏性、聚类和空间相关性，纳入到学习中，并通过高阶卷积模拟交互效应。该研究对神经科学研究信息传递和编码过程中神经元间的协调机制具有重要意义。更重要的是，要开发的模型具有有效和可扩展的计算程序，可以适应时间和空间过程，并适用于其他类型的科学应用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Large-scale point process data is ubiquitous in a wide variety of scientific and business applications, for example in neuroscience. This project aims to develop a sequence of novel statistical methods and machine learning algorithms for modeling high-dimensional point process data. These methods can be used to analyze the complex ensemble neuronal activity data, which is now of key interest in neuroscience to understand mechanisms of sensory coding, motor output, and cognitive function for groups of neurons. The methods will also be useful to address other important scientific questions, such as predicting the occurrence of earthquakes, capturing the spatial pattern of galaxies, characterizing social networks, and modeling marketing forecasts and supply chains. This project will stimulate interdisciplinary collaboration between data and domain scientists from disparate areas including neuroscience, environmental science, business, epidemiology, astronomy, ecology, and political science. The project will integrate research with the teaching and training of students at various levels. Software packages implemented in programming languages R and Python will be developed and distributed for broad use.Analyzing multivariate neuronal spike trains data imposes significant challenges and requires new sophisticated tools for modeling high-dimensional point processes. This project aims to develop a general multivariate point process regression model, which allows both high-dimensional point-process-type responses and predictors, through utilizing the advanced tensor decomposition techniques. The method will enable researchers to model a large number of neurons jointly while having the model dimension substantially reduced—this turns the adversity of the high dimensionality of data into benefits. The project will also incorporate additional structures, such as sparsity, clustering, and spatial-correlation, into learning, and model interaction effects through higher-order convolutions. The research can greatly facilitate neuroscience studies regarding coordinating mechanisms among neurons in information transmission and encoding. More importantly, the models to be developed with effective and scalable computing procedures can adapt to both temporal and spatial processes and apply to other types of scientific applications.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.