同时稀疏和低秩矩阵的估计
Estimation of Simultaneously Sparse and Low Rank Matrices
AI总结：
本文提出一种凸混合惩罚方法，同时使用ℓ1范数和迹范数，以估计同时稀疏和低秩的矩阵，并推导了预言不等式和链接预测的泛化误差界，通过近端下降算法高效求解。
摘要：
本文介绍了一种惩罚矩阵估计过程，旨在同时实现稀疏和低秩的解。这种结构出现在社交网络或蛋白质相互作用的背景下，其中底层图的邻接矩阵在适当基下是块对角化的。我们引入了一种凸混合惩罚，同时涉及ℓ1范数和迹范数。我们得到了一个预言不等式，指示了两种效应如何根据目标矩阵的性质相互作用。我们界定了链接预测问题中的泛化误差。我们还开发了近端下降策略来高效求解优化问题，并在合成和真实数据集上评估了性能。
英文摘要：
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously. We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix. We bound generalization error in the link prediction problem. We also develop proximal descent strategies to solve the optimization problem efficiently and evaluate performance on synthetic and real data sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
