User-Friendly Tail Bounds for Matrix Martingales

2011

50 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3b84c849d05061fc9e64004e4cae2a3c76bbe56a

Citations in the corpus

Introduction to the non-asymptotic analysis of random matrices (2010, unknown): “equalities in probability theory, which was based on trace inequalities like GoldenThompson inequality. A development of this idea leads to remarkably sharp results. We quote one such inequality from [77]: Theorem 29 (Non-commutative Bernstein-type inequality [77]). Consider a ﬁ- nite sequence Xi of”
An Introduction to Matrix Concentration Inequalities (2015, unknown): “The technical report [182] explains how to extend other bounds for a sum of independent random matrices to the martingale setting.”
User-Friendly Tail Bounds for Sums of Random Matrices (2010, unknown): “For more refined martingale inequalities, see the papers [39, 55] and the technical report [57].”
FREEDMAN'S INEQUALITY FOR MATRIX MARTINGALES (2011, unknown): “ other types of probability inequalities for adapted sequence of random matrices. We have dilated on this observation in a preliminary version of this work that is now available as a technical report [Tro11]. Here, for brevity, we focus on proving Freedman’s inequality. 2. Tail Boundsvia MartingaleM”
On the Local Correctness of L^1 Minimization for Dictionary Learning (2011, unknown): “The ﬁrst, which plays a key role, is the matrix Chernoﬀ bound of Tropp [Tro10].”
Recovering Low-Rank Matrices From Few Coefficients in Any Basis (2009, unknown): “A few months after our pre-print appeared, more sophisticated matrix-valued martingale bounds were established in [36].”
A Probabilistic and RIPless Theory of Compressed Sensing (2010, unknown): “Here, we use a more modern technique based on the matrix Bernstein inequality of Ahlswede and Winter [1], developed for this setting by Gross [26], and tightened in [48] by Tropp and in [32] by Oliveira.”
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise (2010, unknown): “The version here is a slight weakening (but suﬃcient for our purposes) of a result due to Recht [22]; we also refer the reader to the notes of Vershynin [31], and the strengthened results provided by Tropp [30].”