基于分布式优化的大数据局部聚集建模：在神经影像学中的应用
Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging
摘要：
技术进步导致了具有矩阵值协变量的结构化大数据的激增。我们特别致力于基于每个受试者的脑成像扫描为多受试者神经成像数据构建预测模型。这是一个超高维的问题，由每个受试者的协变量矩阵（时间点的大脑位置）组成;目前很少有方法将监督模型直接拟合到这个张量数据。我们提出了一种新的建模和算法策略，应用广义线性模型（GLM），这个庞大的张量数据，其中一组变量与位置。我们的方法首先将GLM分别拟合到每个位置，然后通过正则化将位置之间的信息混合起来，并使用我们称之为聚合惩罚来构建一个集合。我们所谓的，局部聚集模型，可以适合在一个完全分布式的方式在位置上使用交替方向乘法（ADMM）的策略，从而大大减少了计算负担。此外，我们建议通过一系列新的更快的算法解决方案来选择合适的模型，这类似于正则化路径。我们将通过模拟和EEG分类问题展示我们的方法的计算和预测建模优势。
英文摘要：
Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.
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