Related papers: Margins, Shrinkage, and Boosting
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin,…
Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation…
Boosting is one of the most significant advances in machine learning for classification and regression. In its original and computationally flexible version, boosting seeks to minimize empirically a loss function in a greedy fashion. The…
Boosting has attracted much research attention in the past decade. The success of boosting algorithms may be interpreted in terms of the margin theory. Recently it has been shown that generalization error of classifiers can be obtained by…
Margin theory provides one of the most popular explanations to the success of \texttt{AdaBoost}, where the central point lies in the recognition that \textit{margin} is the key for characterizing the performance of \texttt{AdaBoost}. This…
We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of AdaBoost, LogitBoost and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems…
In this paper we establish a new margin-based generalization bound for voting classifiers, refining existing results and yielding tighter generalization guarantees for widely used boosting algorithms such as AdaBoost (Freund and Schapire,…
Schapire's margin theory provides a theoretical explanation to the success of boosting-type methods and manifests that a good margin distribution (MD) of training samples is essential for generalization. However the statement that a MD is…
The following work is a preprint collection of formal proofs regarding the convergence properties of the AdaBoost machine learning algorithm's classifier and margins. Various math and computer science papers have been written regarding…
Boosting methods are highly popular and effective supervised learning methods which combine weak learners into a single accurate model with good statistical performance. In this paper, we analyze two well-known boosting methods, AdaBoost…
Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of…
Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that…
As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely…
Boosting is one of the most successful ideas in machine learning, achieving great practical performance with little fine-tuning. The success of boosted classifiers is most often attributed to improvements in margins. The focus on margin…
Well-known for its simplicity and effectiveness in classification, AdaBoost, however, suffers from overfitting when class-conditional distributions have significant overlap. Moreover, it is very sensitive to noise that appears in the…
We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings:…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable…
Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically…
It is known that Boosting can be interpreted as a gradient descent technique to minimize an underlying loss function. Specifically, the underlying loss being minimized by the traditional AdaBoost is the exponential loss, which is proved to…