Boosting With the L2 Loss

By Peter Buhlmann, Bin Yu. 2003

684 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Propensity score estimation with boosted regression for evaluating causal effects in observational studies. (2004, background): “Boosting is particularly effective when the model involves a large set of covariates (Bühlmann & Yu, 2003).”
Boosted trees for ecological modeling and prediction. (2007, methodology): “For small data sets however, the reduction in size of the training data relative to the full data degrades estimates of PE (Hastie et al. 2001), and thus the second approach is to determine the number of trees using cross-validation (Bühlmann and Yu 2003).”
A comparison of methods for the fitting of generalized additive models (2008, background): “Since it has been shown that reweighting corresponds to minimizing iteratively a loss function (Breiman 1999; Friedman 2001) boosting has been extended to regression problems in a L2-estimation framework by Bühlmann and Yu (2003).”
Statistical behavior and consistency of classification methods based on convex risk minimization (2003, background): “In another related work, Buhlmann and Yu investigated various theoretical issues for the least squares formulation of boosting [ 5 ] and argued that the procedure can be as effective as other methods.”
A Modern Take on the Bias-Variance Tradeoff in Neural Networks (2018, background): “In spite of this monotonicity in test error, Bühlmann & Yu (2003) show that variance grows at an exponentially decaying rate, calling this an “exponen-tial bias-variance tradeoﬀ.””
Variable Selection in Predictive Regressions (2013, background): “For example, the L2 boosting of Buhlmann and Yu (2003) restricts successive revisions in β̂j to agree in sign with sgn (corr(Xj , r)).”
Small Area Estimation of the Homeless in Los Angeles: An Application of Cost-Sensitive stochastic Gradient Boosting (2010, background): “t=1 quantile (zti): ( 11 ) Because L1( ) is dierentiable and there exists a solution that minimizes”
Robust LogitBoost and Adaptive Base Class (ABC) LogitBoost (2010, background): “1 Introduction Boosting [14, 5, 6, 1, 15, 8, 13, 7, 4] has been successful in machine learning and industry practice.”
Interpretability is Harder in the Multiclass Setting: Axiomatic Interpretability for Multiclass Additive Models (2018, methodology): “2018) fits GAMs using component-wise gradient boosting (Buhlmann and Yu 2003); pyGAM (Serven and Brummitt 2018) fits GAMs with P-splines base learners using penalized iteratively reweighted least squares.”