Totally Corrective Multiclass Boosting with Binary Weak Learners

In this work, we propose a new optimization framework for multiclass boosting learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two successful multiclass boosting algorithms, which can use binary weak learners. We explicitly derive these two algorithms' Lagrange dual problems based on their regularized loss functions. We show that the Lagrange dual formulations enable us to design totally-corrective multiclass algorithms by using the primal-dual optimization technique. Experiments on benchmark data sets suggest that our multiclass boosting can achieve a comparable generalization capability with state-of-the-art, but the convergence speed is much faster than stage-wise gradient descent boosting. In other words, the new totally corrective algorithms can maximize the margin more aggressively.Comment: 11 page

A Comparison of Multi-instance Learning Algorithms

Motivated by various challenging real-world applications, such as drug activity prediction and image retrieval, multi-instance (MI) learning has attracted considerable interest in recent years. Compared with standard supervised learning, the MI learning task is more difficult as the label information of each training example is incomplete. Many MI algorithms have been proposed. Some of them are specifically designed for MI problems whereas others have been upgraded or adapted from standard single-instance learning algorithms. Most algorithms have been evaluated on only one or two benchmark datasets, and there is a lack of systematic comparisons of MI learning algorithms. This thesis presents a comprehensive study of MI learning algorithms that aims to compare their performance and find a suitable way to properly address different MI problems. First, it briefly reviews the history of research on MI learning. Then it discusses five general classes of MI approaches that cover a total of 16 MI algorithms. After that, it presents empirical results for these algorithms that were obtained from 15 datasets which involve five different real-world application domains. Finally, some conclusions are drawn from these results: (1) applying suitable standard single-instance learners to MI problems can often generate the best result on the datasets that were tested, (2) algorithms exploiting the standard asymmetric MI assumption do not show significant advantages over approaches using the so-called collective assumption, and (3) different MI approaches are suitable for different application domains, and no MI algorithm works best on all MI problems

RandomBoost: Simplified Multi-class Boosting through Randomization

We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.Comment: 15 page

Multi-group support vector machines with measurement costs a biobjective approach

Support Vector Machine has shown to have good performance in many practical classification settings. In this paper we propose, for multi-group classification, a biobjective optimization model in which we consider not only the generalization ability (modelled through the margin maximization), but also costs associated with the features. This cost is not limited to an economical payment, but can also refer to risk, computational effort, space requirements, etc. We introduce a biobjective mixed integer problem, for which Pareto optimal solutions are obtained. Those Pareto optimal solutions correspond to different classification rules, among which the user would choose the one yielding the most appropriate compromise between the cost and the expected misclassification rate.Ministerio de Ciencia y TecnologíaPlan Andaluz de Investigació

Binarized support vector machines

The widely used Support Vector Machine (SVM) method has shown to yield very good results in Supervised Classification problems. Other methods such as Classification Trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in Data Mining. In this work, we propose an SVM-based method that automatically detects the most important predictor variables, and the role they play in the classifier. In particular, the proposed method is able to detect those values and intervals which are critical for the classification. The method involves the optimization of a Linear Programming problem, with a large number of decision variables. The numerical experience reported shows that a rather direct use of the standard Column-Generation strategy leads to a classification method which, in terms of classification ability, is competitive against the standard linear SVM and Classification Trees. Moreover, the proposed method is robust, i.e., it is stable in the presence of outliers and invariant to change of scale or measurement units of the predictor variables. When the complexity of the classifier is an important issue, a wrapper feature selection method is applied, yielding simpler, still competitive, classifiers

Kullback-Leibler aggregation and misspecified generalized linear models

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood maximization and we derive sharp oracle inequalities that hold both in expectation and with high probability. Finally all the bounds are proved to be optimal in a minimax sense.Comment: Published in at http://dx.doi.org/10.1214/11-AOS961 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org