Prediction Games and Arcing Algorithms

By Leo Breiman. 1999

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Citations in the corpus

On the empirical estimation of integral probability metrics (2012, neutral): “See [9, 37] for details.”
Special Invited Paper-Additive logistic regression: A statistical view of boosting (2000, methodology): “In Breiman (1999a), empirical evidence is given to show that AdaBoost is a random forest.”
Boosting With the L2 Loss (2003, background): “This gradient descent view has been recognized and re ned by various authors, including Breiman (1999), Mason et al. (2000), Friedman et al. (2000), and Friedman (2001).”
Boosting with early stopping: Convergence and consistency (2005, methodology): “More recently, it was noticed that the AdaBoost method proposed in the machine learning community [13] can also be regarded as stagewise fitting of additive models under an exponential loss function [7, 8, 15, 31, 34].”
A Boosting Algorithm for Classification of Semi-Structured Text (2004, methodology): “We here use Arc-GV (Breiman, 1999) instead of AdaBoost, since Arc-GV asymptotically maximizes the margin and shows faster convergence to the optimal solution than AdaBoost.”
On the Dual Formulation of Boosting Algorithms (2009, background): “In AdaBoost, one of the main purposes is to control the divergence of the margin distribution, which may not be easy to optimize directly because a margin can take a value out of the range [0 , 1] , where entropy is not applicable.”
Boosting Algorithms as Gradient Descent (1999, methodology): “Step size AdaBoost [9] e (cid:0)yF ( x ) Line search ARC-X4 [2] (1 (cid:0) yF(x)) 1=t Con(cid:12)denceBoost [19] e (cid:0)yF ( x ) Line search LogitBoost [12] ln(1 + e (cid:0)yF ( x ) ) Newton-Raphson convergence guarantees only: in practice they will almost always be smaller than necessary, hence (”
An Introduction to Boosting and Leveraging (2002, methodology): “In contrast to this, the greedy approach is used by the original AdaBoost/Arc-GV algorithm as discussed above: only the weight of the last hypothesis is selected, while minimizing some appropriate cost function [27, 74, 127, 153].”
Functional Frank-Wolfe Boosting for General Loss Functions (2015, methodology): “It is well known that AdaBoost can be derived from functional gradient decent method using exponential loss [1, 27].”
Boosting Algorithms as Gradient Descent in Function Space (2007, methodology): “One way to produce a weighted combination of classiiers which optimizes (1) is by gradient descent in function space, an idea rst proposed by Breiman 4].”
Prototype Classification: Insights from Machine Learning (2009, methodology): “We therefore consider for simplicity the hypothesis set Several iterative methods for solving equation 5.5 have been proposed (Breiman, 1999; Schapire, 2001; Rudin, Daubechies, & Schapire, 2004).”
On Early Stopping in Gradient Descent Learning (2007, background): “For example, studies on both lead a road to game theory [e.g. Breiman 1999; Freund and Schapire 1999; Schapire 2001; Stoltz and Lugosi 2004], on the ﬁrst have been seen in [Rudin, Daubechies, and Schapire 2004] and on the second lead to the functional gradient descent view with general convex loss…”
Advance and Prospects of AdaBoost Algorithm (2013, unknown): “AdaBoost 与博弈理论的联系由 Breiman 、 Freund 和 Schapire 等提出 [16 , 48 − 50] , AdaBoost.”
Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers (2015, background): “However, one can ﬁnd evidence against this hypothesis in Breiman’s arc-gv algorithm (Breiman, 1999).”