Learning Mixtures of Low-Rank Models
Learning Mixtures of Low-Rank Models
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DOI：
10.1109/tit.2021.3065700
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发表时间：
2020-09
影响因子：
2.5
通讯作者：
Yanxi Chen;Cong Ma;H. Poor;Yuxin Chen
中科院分区：
文献类型：
--
作者：
Yanxi Chen;Cong Ma;H. Poor;Yuxin Chen
我们研究了低阶模型的混合学习问题，即从每个低阶模型的无标号线性测量中重构多个低阶矩阵。该问题通过考虑潜在变量(即未知标签)和结构先验(即低阶结构)，丰富了两种被广泛研究的环境--低阶矩阵感知和混合线性回归。针对非标号异质数据和低复杂度结构带来的非凸性问题，提出了一种三阶段元算法，保证在高斯设计下恢复样本和计算复杂度接近最优的未知矩阵。此外，该算法对随机噪声具有较好的稳定性。我们用经验证据来补充理论研究，证实了我们算法的有效性。
We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings — low-rank matrix sensing and mixed linear regression — by bringing latent variables (i.e. unknown labels) and structural priors (i.e. low-rank structures) into consideration. To cope with the non-convexity issues arising from unlabelled heterogeneous data and low-complexity structure, we develop a three-stage meta-algorithm that is guaranteed to recover the unknown matrices with near-optimal sample and computational complexities under Gaussian designs. In addition, the proposed algorithm is provably stable against random noise. We complement the theoretical studies with empirical evidence that confirms the efficacy of our algorithm.