Boosting with the L_2-Loss: Regression and Classification

By Bin Yu. 2001

Subfields: Statistics and Probability, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

In Statistical Learning Theory

Citations in the corpus

Causal inference by using invariant prediction: identification and confidence intervals (2015, methodology): “For example, ˆ B could be the set of variables with non-zero regression coeﬃcient with square-root Lasso estimation [Belloni et al., 2011], Lasso [Tibshirani, 1996] or boosting [Schapire et al., 1998, Friedman, 2001, B¨uhlmann and Yu, 2003] with cross-validated penalty parameter.”
Early stopping for non-parametric regression: An optimal data-dependent stopping rule (2011, background): “(For instance, see the paper by Strand [35], with follow-up work by Anderssen and Prenter [1] as well as Wahba [38].)”
Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution (2018, unknown): “From a broad point of view, discussions on consistency and convergence of general L 2 boosting framework can be found in B¨uhlmann and Yu (2003), Zhang et al. (2005) and B¨uhlmann and Hothorn (2007).”
The Rhetoric and Reality of Anthropomorphism in Artificial Intelligence (2019, background): “Researchers in this area tend to follow a similar strategy to those who study bagging, relying on slight idealizations to derive convergence rates and other relevant theorems (Bühlmann and Hothorn 2007; Bühlmann and Yu 2003; Ehrlinger and Ishwaran 2012).”
Spectral Algorithms for Supervised Learning (2008, methodology): “The gradient descent learning algorithm in Yao et al. (2007) can be seen as an instance of Landwe-ber iteration (Engl et al., 1996) and is related to the L 2 boosting algorithm (B¨uhlmann & Yu, 2002).”
Theory of classification : a survey of some recent advances (2005, background): “Based on this view, various versions of boosting algorithms have been shown to be consistent in different settings, see Breiman [52], Bühlmann and Yu [54], Blanchard, Lugosi, and Vayatis [40], Jiang [111], Lugosi and Vayatis [146], Mannor and Meir [152], Mannor, Meir, and Zhang [153], Zhang [244].”
Model-based Boosting 2.0 (2010, methodology): “The details have been described by Bühlmann and Yu (2003).”
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)).”
Selecting Instrumental Variables in a Data Rich Environment (2009, background): “Component- wise boosting was considered by Buhlmann and Yu (2003) when the number of predictors is large.”