Integrative multi‐view regression: Bridging group‐sparse and low‐rank models
Integrative multi‐view regression: Bridging group‐sparse and low‐rank models
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DOI：
10.1111/biom.13006
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发表时间：
2019-03
期刊：
影响因子：
1.9
通讯作者：
Gen Li;Xiaokang Liu;Kun Chen
中科院分区：
文献类型：
--
作者：
Gen Li;Xiaokang Liu;Kun Chen
在科学和工程的各个领域中，多视图数据已被常规收集。一个普遍的问题是研究多变量响应和多视图预测器集之间的预测关联，所有这些都可以是高维的。很可能只有少数视图与预测相关，并且每个相关视图内的预测因子共同而不是稀疏地对预测做出贡献。我们将这个新问题置于熟悉的多元回归框架下，并提出了一种综合降秩回归（iRRR），其中每个视图都有自己的低秩系数矩阵。因此，以监督的方式从每个视图中提取潜在特征。对于模型估计，我们提出了一种凸复合核范数惩罚方法，该方法通过交替方向乘子法实现了一种有效的算法。讨论了非高斯和不完整数据的扩展。在理论上，我们在限制特征值条件下导出了iRRR的非渐近预言界。我们的结果恢复了iRRR的几个特殊情况下，包括Lasso，组Lasso，核范数惩罚回归的预言界。因此，iRRR无缝地桥接了组稀疏和低秩方法，并且可以在多视图学习的实际设置下实现更快的收敛速度。模拟研究和应用程序中的纵向研究老化进一步展示了所提出的方法的有效性。
Multi‐view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi‐view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced‐rank regression (iRRR), where each view has its own low‐rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non‐Gaussian and incomplete data are discussed. Theoretically, we derive non‐asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso, and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group‐sparse and low‐rank methods and can achieve substantially faster convergence rate under realistic settings of multi‐view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods.