Low-rank spectral estimation algorithm of learning Markov model  

作　　者：Yongye ZHAO Shujun BI 

机构地区：[1]Department of Basic Courses,Guangzhou Maritime University,Guangzhou 510725,China [2]Department of Mathematics,South China University of Technology,Guangzhou 510640,China

出　　处：《Frontiers of Mathematics in China》2024年第3期137-155,共19页中国高等学校学术文摘·数学（英文）

摘　　要：This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipschitzian error bound established.Then,we propose a low-rank spectral estimation algorithm for estimating the state transition frequency matrix and the probability matrix of Markov model by applying the approximate projection algorithm to correct the maximum likelihood estimation of the frequency matrix,and prove that there is only a multiplying constant difference in estimation errors between the low-rank spectral estimation and the maximum likelihood estimation under appropriate conditions.Finally,numerical comparisons with the prevailing maximum likelihood estimation,spectral estimation,and rank-constrained maxi-mum likelihood estimation show that the low-rank spectral estimation algorithm is effective.

关 键 词：Markov model low-rank spectral estimation error bound approximate projection 

分 类 号：O17[理学—数学]