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首页> 外文期刊>IEEE Transactions on Information Theory >SOFAR: Large-Scale Association Network Learning
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SOFAR: Large-Scale Association Network Learning

机译：SOFAR：大规模协会网络学习

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摘要

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper, we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks, such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulations and real data examples.
机译：许多现代大数据应用程序都具有大量的响应和预测变量。通过按重要性排列的稀疏潜在因子层了解大规模响应-预测器关联网络结构，可以提高统计效率和科学见解。然而，稀疏性和正交性是两个主要不兼容的目标。为了适应这两个特征，在本文中，我们建议通过稀疏奇异值分解与正交约束优化来学习底层关联网络的稀疏正交因子回归（SOFAR）方法，广泛应用于无监督和有监督的学习任务，例如包括稀疏奇异值分解，稀疏主成分分析，稀疏因子分析和备用矢量自回归分析。利用凸面辅助非凸优化的框架，我们推导出了非渐近误差界，用于表征理论优势的建议过程。统计保证由具有收敛性的高效SOFAR算法提供支持。我们的程序的计算和理论优势都通过几个模拟和实际数据示例得到了证明。

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