2020/08/12 by Sina Baghal, Baghal, Sina
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2008.05104
openalex publication_date 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a non-asymptotic concentration inequality for the random matrix product Zn = (Id-αXn)(Id-αXn-1)⋯ (Id-αX1), where \Xk \k=1+∞ is a sequence of bounded independent random positive semidefinite matrices with common expectation 𝔼[Xk]=Σ. Under these assumptions, we show that, for small enough positive α, Zn satisfies the concentration inequality ℙ(\Vert Zn-𝔼[Zn]\Vert ≥ t) ≤ 2d2⋅exp((-t2)/(ασ2) ) for all t≥ 0, where σ2 denotes a variance parameter.