Semi-supervised SVMs (S3 VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimization problem is non-convex. To examine the full potential of S3 VMs modulo local minima problems in current implementations, we apply branch and bound techniques for obtaining exact, global ly optimal solutions. Empirical evidence suggests that the globally optimal solution can return excellent generalization performance in situations where other implementations fail completely. While our current implementation is only applicable to small datasets, we discuss variants that can potentially lead to practically useful algorithms.

Recent analyses (Bengio, Delalleau, & Le Roux, 2006; Bengio & Le Cun, 2007) of modern nonparametric machine learning algorithms that are kernel machines, such as Support Vector Machines (SVMs), graph-based manifold and semi-supervised learning algorithms suggest fundamental limitations of some learning algorithms. The problem is clear in kernel-based approaches when the kernel is "local" (e.g., the Gaussian kernel), i.e., K (x, y) converges to a constant when x - y increases. These analyses point to the difficulty of learning "highly-varying functions", i.e., functions that have a large number of "variations" in the domain of interest, e.g., they would require a large number of pieces to be well represented by a piecewise-linear approximation. Since the number of pieces can be made to grow exponentially with the number of factors of variations in the input, this is connected with the well-known curse of dimensionality for classical non-parametric learning algorithms (for regression, classification and density estimation). If the shapes of all these pieces are unrelated, one needs enough examples for each piece in order to generalize properly.

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.

Many tasks in speech processing involve classification of long term characteristics of a speech segment such as language, speaker, dialect, or topic. A natural technique for determining these characteristics is to first convert the input speech into a sequence of tokens such as words, phones, etc. From these tokens, we can then look for distinctive phrases, keywords, that characterize the speech. In many applications, a set of distinctive keywords may not be known a priori. In this case, an automatic method of building up keywords from short context units such as phones is desirable. We propose a method for construction of keywords based upon Support Vector Machines.

We consider the problem of Support Vector Machine transduction, which involves a combinatorial problem with exponential computational complexity in the number of unlabeled examples. Although several studies are devoted to Transductive SVM, they suffer either from the high computation complexity or from the solutions of local optimum. To address this problem, we propose solving Transductive SVM via a convex relaxation, which converts the NP-hard problem to a semi-definite programming. Compared with the other SDP relaxation for Transductive SVM, the proposed algorithm is computationally more efficient with the number of free parameters reduced from O(n2) to O(n) where n is the number of examples. Empirical study with several benchmark data sets shows the promising performance of the proposed algorithm in comparison with other state-of-the-art implementations of Transductive SVM.

This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d. On the practical side, we give a support vector machine (s.v.m.) algorithm for arbitrary c.p.d. For the thin- plate kernel this leads to a classifier with only one parameter (the amount of regu- larisation), which we demonstrate to be as effective as an s.v.m. with the Gaussian kernel, even though the Gaussian involves a second parameter (the length scale).

In this paper, we propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our method simultaneously finds the support vectors and a proxy kernel matrix used in computing the loss. This can be interpreted as a robust classification problem where the indefinite kernel matrix is treated as a noisy observation of the true positive semidefinite kernel. Our formulation keeps the problem convex and relatively large problems can be solved efficiently using the analytic center cutting plane method. We compare the performance of our technique with other methods on several data sets.

We propose a randomized algorithm for large scale SVM learning which solves the problem by iterating over random subsets of the data. Crucial to the algorithm for scalability is the size of the subsets chosen. In the context of text classification we show that, by using ideas from random projections, a sample size of O(log n) can be used to obtain a solution which is close to the optimal with a high probability. Experiments done on synthetic and real life data sets demonstrate that the algorithm scales up SVM learners, without loss in accuracy.

Using multiple regularization hyperparameters is an effective method for managing model complexity in problems where input features have varying amounts of noise. While algorithms for choosing multiple hyperparameters are often used in neural networks and support vector machines, they are not common in structured prediction tasks, such as sequence labeling or parsing. In this paper, we consider the problem of learning regularization hyperparameters for log-linear models, a class of probabilistic models for structured prediction tasks which includes conditional random fields (CRFs). Using an implicit differentiation trick, we derive an efficient gradient-based method for learning Gaussian regularization priors with multiple hyperparameters. In both simulations and the real-world task of computational RNA secondary structure prediction, we find that multiple hyperparameter learning provides a significant boost in accuracy compared to models learned using only a single regularization hyperparameter.

In this paper lower and upper bounds for the number of support vectors are derived for support vector machines (SVMs) based on the epsilon-insensitive loss function. It turns out that these bounds are asymptotically tight under mild assumptions on the data generating distribution. Finally, we briefly discuss a trade-off in epsilon between sparsity and accuracy if the SVM is used to estimate the conditional median.