Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

In this paper, we consider semi-supervised classification on evolutionary data, where the distribution of the data and the underlying concept that we aim to learn change over time due to short-term noises and long-term drifting, making a single aggregated classifier inapplicable for long-term classification. The drift is smooth if we take a localized view over the time dimension, which enables us to impose temporal smoothness assumption for the learning algorithm. We first discuss how to carry out such assumption using temporal regularizers defined in a structural way with respect to the Hilbert space, and then derive the online algorithm that efficiently finds the closed-form solution to the classification functions. Experimental results on real-world evolutionary mailing list data demonstrate that our algorithm outperforms classical semi-supervised learning algorithms in both algorithmic stability and classification accuracy.

We study the problem of learning an optimal subset from a larger ground set of items, where the optimality criterion is defined by an unknown preference function. We model the problem as a discriminative structural learning problem and solve it using a Structural Support Vector Machine (SSVM) that optimizes a set accuracy performance measure representing set similarities. Our approach departs from previous approaches since we do not explicitly learn a pre-defined preference function. Experimental results on both a synthetic problem domain and a real-world face image subset selection problem show that our method significantly outperforms previous learning approaches for such problems.

Most accurate predictions are typically obtained by learning machines with complex feature spaces (as e.g. induced by kernels). Unfortunately, such decision rules are hardly accessible to humans and cannot easily be used to gain insights about the application domain. Therefore, one often resorts to linear models in combination with variable selection, thereby sacrificing some predictive power for presumptive interpretability. Here, we introduce the Feature Importance Ranking Measure (FIRM), which by retrospective analysis of arbitrary learning machines allows to achieve both excellent predictive performance and superior interpretation. In contrast to standard raw feature weighting, FIRM takes the underlying correlation structure of the features into account. Thereby, it is able to discover the most relevant features, even if their appearance in the training data is entirely prevented by noise. The desirable properties of FIRM are investigated analytically and illustrated in simulations.

Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features within a kernel with a sparse set of weights that are estimated in conjunction with the original classification or regression problem. The iterative algorithm, KNIFE, alternates between finding the coefficients of the original problem and finding the feature weights through kernel linearization. In addition, a slight modification of KNIFE yields an efficient algorithm for finding feature regularization paths, or the paths of each feature's weight. Simulation results demonstrate the utility of KNIFE for both kernel regression and support vector machines with a variety of kernels. Feature path realizations also reveal important non-linear correlations among features that prove useful in determining a subset of significant variables. Results on vowel recognition data, Parkinson's disease data, and microarray data are also given.

A discriminative large margin classifier based approach to anaphora resolution for neuroscience abstracts is presented. The system employs both syntactic and semantic features. A support vector machine based word sense disambiguation method combining evidence from three methods, that use WordNet and Wikipedia, is also introduced and used for semantic features. The support vector machine anaphora resolution classifier with probabilistic outputs achieved almost four-fold improvement in accuracy over the baseline method.

For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. Most of the currently used algorithms are not robust in the sense that they cannot deal with general or degenerate input. Here we present a new robust, generic method for parametric quadratic programming. Our algorithm directly applies to nearly all machine learning applications, where so far every application required its own different algorithm. We illustrate the usefulness of our method by applying it to a very low rank problem which could not be solved by existing path tracking methods, namely to compute part-worth values in choice based conjoint analysis, a popular technique from market research to estimate consumers preferences on a class of parameterized options.

This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by Ben-David et al. (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive novel generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularization-based algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give novel algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.

We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/ɛ) steps to ɛ precision for general convex problems and in O(log(1/ɛ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.

To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user specified shiftinvariant kernel. We explore two sets of random features, provide convergence bounds on their ability to approximate various radial basis kernels, and show that in large-scale classification and regression tasks linear machine learning algorithms applied to these features outperform state-of-the-art large-scale kernel machines.