Optimal aggregation of classifiers in statistical learning

By Alexandre B. Tsybakov. 2003

816 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Smoothness, Low Noise and Fast Rates (2010, background): “For example, Steinwart [29] used Local Rademacher Complexity to provide fast rate on the 0/1 loss of Support Vector Machines (SVMs) ( ℓ 2 -regularized hinge-loss minimization) based on the so called “geometric margin condition” and Tsybakov’s margin condition.”
Variance-based Regularization with Convex Objectives (2016, background): “Bounds that trade between risk and variance are known in a number of cases in the empirical risk minimization literature [15, 22, 2, 1, 6, 3, 7, 12], which is relevant when one wishes to achieve “fast 2”
PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES (2011, background): “3) is similar to the margin condition in classification [18, 24, 32]; in classification this assumption is often used to obtain sharp upper bounds on the excess 0–1 risk in terms of other surrogate risks [2].”
Optimization Methods for Large-Scale Machine Learning (2016, background): “For instance, when the loss function is strongly convex [89] or when the data distribution satisfies certain assumptions [147], it is possible to show that E(n, ) = O ( log(n) n + ) .”
Rates of convergence in active learning (2011, background): “If the disagreement coefficient is relatively small, Theore m 4 can represent a significant improvement in convergence rate compared to pas sive learning, where we typically expect rates of order n−κ/(2κ−1) [7, 18, 20]; this gap is especially notable when the disagreement coefficient is a finite con”
Online Decision Making with High-Dimensional Covariates (2020, methodology): “This condition is widely used in the classification literature (e.g. Tsybakov (2004)) as well as in Goldenshluger et al. (2013).”
Classification with reject option (2006, background): “Bartlett and Mendelson (2003) call a class F that satisfies Eg(2) f,d(X, Y ) ≤ B {gf,d(X, Y )} β for all f ∈ F , (21)”
Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice (2015, methodology): “This lemma follows from Theorem 2.14.9 in van der Vaart and Wellner (1996) combined with their Theorem 2.6.4.”
Learning Theory Estimates via Integral Operators and Their Approximations (2007, methodology): “To this end, we introduce a function motivated by the Tsybakov condition [12] with noise exponent q(0 < q ≤ ∞): for some constant cq > 0,”
The multi-armed bandit problem with covariates (2011, methodology): “[17, 21], which drives the terminology employed here.”
Classification with a Reject Option using a Hinge Loss (2008, methodology): “…error term ε n approaches zero at a faster rate when the conditional probability η(X) is unlikely to be close to the critical value of 1/2 (Audibert and Tsybakov, 2007; Bartlett et al., 2006; Blanchard et al., 2008; Steinwart and Scovel, 2007; Tarigan and van de Geer, 2006; Tsybakov, 2004).”
Fast learning rates for plug-in classifiers (2005, background): “A standard complexity assumption on the decision set (CAD) is the following.”
Improvability Through Semi-Supervised Learning: A Survey of Theoretical Results (2019, methodology): “Such requirement on P (Y |X) is very similar to the Tsybakov-margin condition [Tsybakov, 2004], which is used in statistical learning to come to fast learning rates.”
Faster Rates for Policy Learning (2017, background): “Hence, the minimax rate is not faster than n unless one constrains the class of distributions to which P can belong via a margin condition (see [23, 11]).”
STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY (2016, background): “This assumption is a direct restatement of Assumption (MA) from Audibert and Tsybakov (2007) and was considered earlier by Tsybakov (2004). Note that this theorem is similar in spirit to Lemma 1 in van der Laan and Luedtke (2014b), but relies on weaker, and we believe more interpretable, assumptions”
Risk bounds for statistical learning (2007, background): “In [ 22 ], Tsybakov attracted attention to rates faster than 1/ √ n that can be achieved by the ERM esti-”
A Classification Framework for Anomaly Detection (2005, background): “[29], [24]) as the following proposition which is proved in the appendix shows:”
Action-Gap Phenomenon in Reinforcement Learning (2011, result): “If this condition holds, “fast” convergence rate is obtainable as was shown by Mammen and Tsybakov [3], Tsybakov [4], Audibert and Tsybakov [5].”