Inégalités de concentration pour les processus empiriques de classes de parties

By E. Rio. 2001

70 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c1e864c79ad75932522f798ab5f34ffc39f6932f

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Citations in the corpus

Concentration Inequalities (2008, methodology): “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].”
On concentration of self-bounding functions (2009, methodology): “This inequality is at the basis of several concentration inequalities proved by the entropy method, see [2, 3, 17, 16, 4, 11, 13].”
A high-dimensional Wilks phenomenon (2011, methodology): “…E h Pn−1bhn−1i ≥ E hPnbhni . ut Remark 1 Note that we refrained from using the immediate upper-bounds Pnbh2n ≤ sup h∈H Pnh 2 or Pbh2n ≤ sup h∈H Ph2 as is usually done in the proof of the above-stated upper-bounds on the variance of suprema of general empirical processes (Rio 2001; Bousquet 2003).”
Compressive Sensing with structured random matrices (2012, background): “The constants in the deviation and concentration inequalities were successfully improved in [85, 107, 108, 14, 77].”
Convexity, Classification, and Risk Bounds (2006, methodology): “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).”
Theory of classification : a survey of some recent advances (2005, unknown): “For various improvements, see Ledoux [132], Massart [159], Rio [184].”
Moment inequalities for functions of independent random variables (2005, methodology): “Ledoux’s method relies on abstract functional inequalities known as logarithmic Sobolev inequalities and provides a powerful tool for deriving exponential inequalities for functions of independent random variables; see [6, 7, 8, 14, 30, 31, 36] for various applications.”
Concentration inequalities using the entropy method (2003, methodology): “A novel way of deriving powerful inequalities, the “entropy method”, based on logarithmic Sobolev inequalities, was developed by Ledoux [17],[16], Bobkov and Ledoux [3], Massart [24], Rio [28], and Bousquet [5] for proving sharp concentration bounds for maxima of empirical processes.”