Rademacher averages and phase transitions in Glivenko-Cantelli classes

By Shahar Mendelson. 2002

95 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology, Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Smoothness, Low Noise and Fast Rates (2010, background): “where K < 10(5) is a numeric constant derived from [20] and [6].”
On the optimal estimation of probability measures in weak and strong topologies (2013, neutral): “Therefore, by [1, Theorem 11.12], we obtain fat ǫ ( G ) ≤ 1 + ⌊ ǫ − 1 ⌋ and [25, Theorem 3.2] ensures that there exists a universal constant c ′ such that for every empirical measure P n , and every ǫ > 0, thereby yielding the result.”
On the empirical estimation of integral probability metrics (2012, background): “3], in turn based on the bound in [28]; also see [51, Theorem 16]) that bounds Rmn in terms of the entropy number of F, which is then used in Corollary 3.”
Rademacher and Gaussian Complexities: Risk Bounds and Structural Results (2003, neutral): “This result is essentially in (Mendelson, 2002); although that paper gave a result in terms of the fat-shattering dimension, the same proof works for the empirical fat-shattering dimension.”
Local Rademacher complexities (2005, methodology): “upremum of the empirical process (thanks to symmetrization inequalities), it was ﬁrst proposed as an eﬀective complexity measure by Koltchinskii [15], Bartlett, Boucheron and Lugosi [1] and Mendelson [25] and then further studied in [3]. Unfortunately, one of the shortcomings of the Rademacher avera”
Rademacher Chaos Complexities for Learning the Kernel Problem (2010, unknown): “gif" alt-version="no" mimetype="image" xlink:type="simple"> Then we use the following Dudley's entropy bound (Mendelson, 2002 , 2003 ).”
Multi-instance learning with any hypothesis class (2011, methodology): “We have (Bartlett and Mendelson, 2002) Thus we can apply Theorem 20 with β = 0 .”
Learning with Decision Lists of Data-Dependent Features (2005, background): “…class of functions but with features that are not constrained to be identified by pairs or triples of training examples, why not use the well-knownVapnik-Chervonenkis (VC) bounds (Vapnik, 1998) or Rademacher bounds (Mendelson, 2002) to characterize the learning algorithms discussed in this paper?”