Structured matrix learning under arbitrary entrywise dependence and estimation of Markov transition kernel
任意元素依赖下的结构化矩阵学习与马尔可夫转移核估计
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any joint distribution with arbitrary dependence across entries. We propose an incoherent-constrained least-square estimator and prove its tightness both in the sense of deterministic lower bound and matching minimax risks under various noise…