This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation withvarious interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

We consider the problem of detecting humans and classifying their pose from a single image. Specifically, our goal is to devise a statistical model that simultaneously answerstwo questions: 1) is there a human in the image?

We consider the task of tuning hyperparameters in SVM models based on minimizing a smooth performance validation function, e.g., smoothed k-fold cross-validation error, using nonlineaI optimization techniques.

VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimizationproblem is non-convex.

Maximum margin clustering was proposed lately and has shown promising performance in recent studies [1, 2]. It extends the theory of support vector machineto unsupervised learning. Despite its good performance, there are three major problems with maximum margin clustering that question its efficiency for real-world applications. First, it is computationally expensive anddifficult to scale to large-scale datasets because the number of parameters in maximum margin clustering is quadratic in the number of examples. Second, it requires data preprocessing to ensure that any clustering boundarywill pass through the origins, which makes it unsuitable for clustering unbalanced dataset. Third, it is sensitive to the choice of kernel functions, and requires external procedure to determine the appropriate values for the parameters of kernel functions. In this paper, we propose "generalized maximum margin clustering" framework that addresses the above three problems simultaneously.

The theoretical understanding of support vector machines (SVMs) and related kernel-based methods has been substantially improved in recent years.

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.

A geometric framework for understanding multi-category classification is introduced, through which many existing 'all-together' algorithms can be understood. The structure enables parsimonious optimisation, through a direct extension of the binary methodology. The focus is on Support Vector Classification, with parallels drawn to related methods. The ability of the framework to compare algorithms is illustrated by a brief discussion of Fisher consistency. Its utility in improving understanding of multi-category analysis is demonstrated through a derivation of improved generalisation bounds. It is also described how this architecture provides insights regarding how to further improve on the speed of existing multi-category classification algorithms. An initial example of how this might be achieved is developed in the formulation of a straightforward multi-category Sequential Minimal Optimisation algorithm. Proof-of-concept experimental results have shown that this, combined with the mapping of pairwise results, is comparable with benchmark optimisation speeds.

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind these two types of methods, namely how to transform linear algorithms into nonlinear ones by using kernel functions, and how to make predictions with an ensemble or a collection of models rather than a single model. I also share my personal perspectives on how these ideas have influenced and shaped my own research. In particular, I present two recent algorithms that I have invented with my collaborators: LAGO, a fast kernel algorithm for unbalanced classification and rare target detection; and Darwinian evolution in parallel universes, an ensemble method for variable selection.