Boosting with the L2-loss: regression and classification

By Peter Buhlmann, Bin Yu. 2001

471 citations recorded by the source corpus.

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In Artificial Intelligence

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.”
Fused Lasso Additive Model (2014, background): “Flexible additive modeling in high dimensions has been an active area of research in recent years (Bühlmann and Yu 2003; Sardy and Tseng 2004; Lin and Zhang 2006; Avalos, Grandvalet, and Ambroise 2007; Bühlmann and Hothorn 2007; Huang, Horowitz, and Wei 2010; Zhang, Cheng, and Liu 2011; Wood, Goude,”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, methodology): “We implement this with a boosting method for additive model fitting [2, 5], using the R-function gamboost from the package mboost [9].”
High-dimensional additive modeling (2008, methodology): “Our new approach with the sparsity and smoothness penalty is never worse and some-times substantially better than L 2 -boosting for generalized additive model ﬁtting [ 5, 7].”
Learning Global Additive Explanations for Neural Nets Using Model Distillation (2018, methodology): “For trees we use cyclic gradient boosting [7, 28] which learns the feature shapes in a cyclic manner.”
An Introduction to Boosting and Leveraging (2002, unknown): “[76, 158, 62, 18, 31, 3, 155, 15, 44, 52, 82, 164, 66, 38, 137, 147, 16, 80, 185, 100, 14].”
Conditional transformation models (2012, methodology): “The boosting algorithm presented here is a variant of L2WCBoost (Bühlmann and Yu 2003) applied to dependent observations with more general base-learners.”
A note on margin-based loss functions in classification (2004, background): “B¨uhlmann and Yu (2001) studied the properties of boosting with the square loss (called L 2 Boost in that paper).”
Estimation Stability With Cross-Validation (ESCV) (2013, methodology): “Regularization methods can also take the form of early stopping iterative algorithms like classical forward selection or L 2 -Boosting (Friedman 2001; B¨uhlmann and Yu 2003; Zhang and Yu 2012; Zhang 2011).”
Boosting for high-dimensional linear models (2006, methodology): “1, and other supporting empirical results have been reported in [3] in the different context of low- or high-dimensional additive models for comparing L2Boosting with more traditional methods such as backfitting or MARS (restricted to additive function estimates).”
Penalized Regression with Ordinal Predictors (2009, methodology): “Today Tukey’s reroughing, resp. twicing is often seen as a predecessor of boosting, see for example Schapire (1990), Freund (1995), Freund & Schapire (1996), or Bühlmann & Yu (2003).”
Early stopping for non-parametric regression: An optimal data-dependent stopping rule (2011, methodology): “Our proof is based on a combination of analytic techniques [10] with techniques from empirical process theory [36].”
Reconciling modern machine learning and the bias-variance trade-off (2018, methodology): “A similar phenomenon is observed using L2-boosting with decision trees [13, 9], as reported in Appendix E.”
Forest Garrote (2009, background): “Another example of tree ensembles are boosted regression trees (Yu and Bühlmann, 2003).”
Model-Based Recursive Partitioning (2008, background): “The latter is of diminishing importance because modern approaches to predictive modeling such as boosting (e.g., simple L 2 boosting by B¨uhlmann and Yu 2003), random forests (Breiman 2001) or support vector machines (Vapnik 1996) are often found to be superior to trees in purely predictive…”
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 [242].”
Generalized Dictionary for Multitask Learning with Boosting (2016, background): “This yields an L2boostingtype [Bühlmann and Yu, 2003] dictionary learning algorithm.”