About the constants in Talagrand's concentration inequalities for empirical processes

2000

247 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9ac676e71dafc3df015c7a3b5584b0c1c966ad84

Citations in the corpus

• The Partial Linear Model in High Dimensions (2013, unknown): “Therefore, for all t > 0, by Massart’s inequality Massart (2000), (see also Corollary 14.”
• Concentration Inequalities (2008, unknown): “In this section we focus on so-called “entropy method”, based on logarithmic Sobolev inequalities developed by Ledoux [20, 21], see also Bobkov and Ledoux [22], Massart [23], Rio [10], Boucheron, Lugosi, and Massart [25], [26], and Bousquet [27, 28].”
• Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results (2006, unknown): “t has been done before several times). This yields a bound of the order Cδ n, which also tends to 0. Combining the above bounds establishes (5.4). One of the versions of Talagrand’s inequality (e.g., [10]) together with (5.5) gives with some constant K > 0 and with probability at least 1− e−t 1 n”
• A Few Notes on Statistical Learning Theory (2002, unknown): “This " functional " inequality was first established by Talagrand [33], and later was modified and partially improved by Ledoux [15], Massart [18], Rio [28] and Bousquet [3].”
• A high-dimensional Wilks phenomenon (2011, unknown): “The possibility to derive interesting bounds (fast rates) for the excess risk critically relies on the next assumption (Mammen and Tsybakov 1999; Massart 2000b; Koltchinskii 2006; Bartlett and Mendelson 2006; Massart 2007; Boucheron et al. 2005a).”
• Convexity, Classification, and Risk Bounds (2006, unknown): “We use the following concentration inequality, which is a refinement, due to Rio (2001) and Klein (2002), of a result of Massart (2000a), following Talagrand (1994) and Ledoux (2001).”
• Sparsity and incoherence in compressive sampling (2006, unknown): “We note that very precise values of the numerical constant K are known and are small, see [23] and [19, 24].”
• Theory of classification : a survey of some recent advances (2005, unknown): “Both approaches use a version of the peeling technique, but the one of Massart uses in addition a weighting approach.”
• Regularization in kernel learning (2010, unknown): “The version of this concentration results we shall use here is due to Massart [ 17 ].”
• Exponential Inequalities, with Constants, for U-statistics of Order Two (2003, unknown): “To prove this lemma, we use Talagrand's inequality [16] for empirical processes , and more precisely the version with constants obtained by Massart [11] (see also Ledoux [10]).”
• Moment inequalities for functions of independent random variables (2005, unknown): “These modifiedφ-Sobolev/Efron–Stein inequalities play a role similar to the one played by modified log-Sobolev inequalities in the entropy method in [26–28] and [30].”