Concentration Inequalities

By Gábor Lugosi. Annual Conference Computational Learning Theory, 2008

1,027 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fe6f73c286b81db7c36598285995a9ee34c1a2c9

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Citations in the corpus

Multiple Kernel Learning from Noisy Labels by Stochastic Programming (2012, methodology): “The proposition follows directly from the Hoeffding’s inequality (Boucheron et al., 2004).”
Concentration inequalities for order statistics (2012, positive): “Finally, using Hoeffding’s inequality [1] in a crude way leads to E[0 ∧ 1/N ] ≤ exp(−n/8) + 4/n ≤ 8/n.”
Fundamentals of Stein's method (2011, background): “The study of concentration inequalities have a long history and have also found recent use in machine learning and analysis of algorithms - see [16] and references therein for a flavor of the modern considerations of these types of problems.”
A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data (2014, methodology): “…of the American Statistical Association June 2014, Vol. 109, No. 506, Theory and Methods DOI: 10.1080/01621459.2013.866899 661 bootstrap methods, Kerkyacharian, Nickl, and Picard (2012) established a nonasymptotic SCC via concentration inequalities, while another strand of literature…”
Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, methodology): “6 in Boucheron et al. (2013). The theorem states that if Z = (Z1, .”
Sharp nonasymptotic bounds on the norm of random matrices with independent entries (2014, methodology): “As the ﬁrst inequality follows from Gaussian concentration [6, Theorem 5.8] and Theorem 1.1.”
On the sub-Gaussianity of the Beta and Dirichlet distributions (2017, background): “…proxy variance for discrete random variables like the Bernoulli distribution (Buldygin and Moskvichova, 2013; Kearns and Saul, 1998; Berend and Kontorovich, 2013) and the missing mass (McAllester and Schapire, 2000; McAllester and Ortiz, 2003; Berend and Kontorovich, 2013; Ben-Hamou et al., 2017).”
Kantorovich duality for general transport costs and applications (2014, methodology): “We refer to the book by Boucheron, Lugosi and Massart [15] for more development in this ﬁeld.”
Spectral Method and Regularized MLE Are Both Optimal for Top-$K$ Ranking (2017, neutral): “This section collects two standard concentration inequalities used throughout the paper, which can be easily found in textbooks such as Boucheron et al. (2013).”
Sparsity and incoherence in compressive sampling (2006, background): “Proof The proof is essentially an application of Hoeffding’s inequality [2].”
High-dimensional Bayesian inference via the unadjusted Langevin algorithm (2016, methodology): “Our main tool is the Gaussian Poincar´e inequality [3, Theorem 3.20] which can be applied to R γ ( y, · ) deﬁned by (6), noticing that R γ ( y, · ) is a Gaussian distribution with mean y − γ U ( y ) and covariance matrix 2 γ I d : for all Lipschitz function g : where Q n,pγ is given by (7) .”
Optimal errors and phase transitions in high-dimensional generalized linear models (2017, background): “The reader can refer to [102] (Chapter 3) for detailed proofs of these statements.”