807 research outputs found
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
Positive Semidefinite Metric Learning Using Boosting-like Algorithms
The success of many machine learning and pattern recognition methods relies
heavily upon the identification of an appropriate distance metric on the input
data. It is often beneficial to learn such a metric from the input training
data, instead of using a default one such as the Euclidean distance. In this
work, we propose a boosting-based technique, termed BoostMetric, for learning a
quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance
metric requires enforcing the constraint that the matrix parameter to the
metric remains positive definite. Semidefinite programming is often used to
enforce this constraint, but does not scale well and easy to implement.
BoostMetric is instead based on the observation that any positive semidefinite
matrix can be decomposed into a linear combination of trace-one rank-one
matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak
learners within an efficient and scalable boosting-based learning process. The
resulting methods are easy to implement, efficient, and can accommodate various
types of constraints. We extend traditional boosting algorithms in that its
weak learner is a positive semidefinite matrix with trace and rank being one
rather than a classifier or regressor. Experiments on various datasets
demonstrate that the proposed algorithms compare favorably to those
state-of-the-art methods in terms of classification accuracy and running time.Comment: 30 pages, appearing in Journal of Machine Learning Researc
Totally corrective boosting algorithm and application to face recognition
Boosting is one of the most well-known learning methods for building highly accurate classifiers or regressors from a set of weak classifiers. Much effort has been devoted to the understanding of boosting algorithms. However, questions remain unclear about the success of boosting.
In this thesis, we study boosting algorithms from a new perspective. We started our research by empirically comparing the LPBoost and AdaBoost algorithms. The result and the corresponding analysis show that, besides the minimum margin, which is directly and globally optimized in LPBoost, the margin distribution plays a more important role. Inspired by this observation, we theoretically prove 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 of these boosting algorithms, we show that the success of boosting algorithms can be understood in terms of maintaining a better margin distribution by maximizing margins and at the same time controlling the margin variance. We further point out that AdaBoost approximately maximizes the average margin, instead of the minimum margin. The duality formulation also enables us to develop column-generation based optimization algorithms, which are totally corrective. The new algorithm, which is termed AdaBoost-CG, exhibits almost identical classification results to those of standard stage-wise additive boosting algorithms, but with much faster convergence rates. Therefore, fewer weak classifiers are needed to build the ensemble using our proposed optimization technique.
The significance of margin distribution motivates us to design a new column-generation based algorithm that directly maximizes the average margin while minimizes the margin variance at the same time. We term this novel method MDBoost and show its superiority over other boosting-like algorithms. Moreover, consideration of the primal and dual problems together leads to important new insights into the characteristics of boosting algorithms. We then propose a general framework that can be used to design new boosting algorithms. A wide variety of machine learning problems essentially minimize a regularized risk functional. We show that the proposed boosting framework, termed AnyBoostTc, can accommodate various loss functions and different regularizers in a totally corrective optimization way. A large body of totally corrective boosting algorithms can actually be solved very efficiently, and no sophisticated convex optimization solvers are needed, by solving the primal rather than the dual. We also demonstrate that some boosting algorithms like AdaBoost can be interpreted in our framework, even their optimization is not totally corrective, .
We conclude our study by applying the totally corrective boosting algorithm to a long-standing computer vision problem-face recognition. Linear regression face recognizers, constrained by two categories of locality, are selected and combined within both the traditional and totally corrective boosting framework. To our knowledge, it is the first time that linear-representation classifiers are boosted for face recognition. The instance-based weak classifiers bring some advantages, which are theoretically or empirically proved in our work. Benefiting from the robust weak learner and the advanced learning framework, our algorithms achieve the best reported recognition rates on face recognition benchmark datasets
On the Dual Formulation of Boosting Algorithms
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 of these boosting algorithms, we show that the success of
boosting algorithms can be understood in terms of maintaining a better margin
distribution by maximizing margins and at the same time controlling the margin
variance.We also theoretically prove that, approximately, AdaBoost maximizes
the average margin, instead of the minimum margin. The duality formulation also
enables us to develop column generation based optimization algorithms, which
are totally corrective. We show that they exhibit almost identical
classification results to that of standard stage-wise additive boosting
algorithms but with much faster convergence rates. Therefore fewer weak
classifiers are needed to build the ensemble using our proposed optimization
technique.Comment: 16 pages. To publish/Published in IEEE Transactions on Pattern
Analysis and Machine Intelligence, 201
Boosting through Optimization of Margin Distributions
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 explicitly taking the margin distribution of the training data
into account. Most of the current boosting algorithms in practice usually
optimizes a convex loss function and do not make use of the margin
distribution. In this work we design a new boosting algorithm, termed
margin-distribution boosting (MDBoost), which directly maximizes the average
margin and minimizes the margin variance simultaneously. This way the margin
distribution is optimized. A totally-corrective optimization algorithm based on
column generation is proposed to implement MDBoost. Experiments on UCI datasets
show that MDBoost outperforms AdaBoost and LPBoost in most cases.Comment: 9 pages. To publish/Published in IEEE Transactions on Neural
Networks, 21(7), July 201
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