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

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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.