Gaussian process regression allows a simple analytical treatment of exact Bayesian inference and has been found to provide good performance, yet scales badly with the number of training data. In this paper we compare several approaches towards scaling Gaussian processes regression to large data sets: the subset of representers method, the reduced rank approximation, online Gaussian processes, and the Bayesian committee machine. Furthermore we provide theoretical insight into some of our experimental results. We found that subset of representers methods can give good and particularly fast predictions for data sets with high and medium noise levels. On complex low noise data sets, the Bayesian committee machine achieves significantly better accuracy, yet at a higher computational cost.

We propose probabilistic generative models, called parametric mixture models (PMMs), for multiclass, multi-labeled text categorization problem. Conventionally, the binary classification approach has been employed, in which whether or not text belongs to a category is judged by the binary classifier for every category. In contrast, our approach can simultaneously detect multiple categories of text using PMMs. We derive efficient learning and prediction algorithms for PMMs. We also empirically show that our method could significantly outperform the conventional binary methods when applied to multi-labeled text categorization using real World Wide Web pages.

Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this paper is the construction of biologically-motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach using the Spikernel and various standard kernels for the task of predicting hand movement velocities from cortical recordings. In all of our experiments all the kernels we tested outperform the standard scalar product used in regression with the Spikernel consistently achieving the best performance.

Classification with partially labeled data requires using a large number of unlabeled examples (or an estimated marginal P (x)), to further constrain the conditional P (y x) beyond a few available labeled examples. We formulate a regularization approach to linking the marginal and the conditional in a general way. The regularization penalty measures the information that is implied about the labels over covering regions. No parametric assumptions are required and the approach remains tractable even for continuous marginal densities P (x). We develop algorithms for solving the regularization problem for finite covers, establish a limiting differential equation, and exemplify the behavior of the new regularization approach in simple cases.

We introduce a general family of kernels based on weighted transducers or rational relations, rational kernels, that can be used for analysis of variable-length sequences or more generally weighted automata, in applications such as computational biology or speech recognition. We show that rational kernels can be computed efficiently using a general algorithm of composition of weighted transducers and a general single-source shortest-distance algorithm. We also describe several general families of positive definite symmetric rational kernels. These general kernels can be combined with Support Vector Machines to form efficient and powerful techniques for spoken-dialog classification: highly complex kernels become easy to design and implement and lead to substantial improvements in the classification accuracy. We also show that the string kernels considered in applications to computational biology are all specific instances of rational kernels.

There exist many approaches to clustering, but the important issue of feature selection, i.e., selecting the data attributes that are relevant for clustering, is rarely addressed. Feature selection for clustering is difficult due to the absence of class labels. We propose two approaches to feature selection in the context of Gaussian mixture-based clustering. In the first one, instead of making hard selections, we estimate feature saliencies. An expectation-maximization (EM) algorithm is derived for this task. The second approach extends Koller and Sahami's mutual-informationbased feature relevance criterion to the unsupervised case. Feature selection is then carried out by a backward search scheme. This scheme can be classified as a "wrapper", since it wraps mixture estimation in an outer layer that performs feature selection. Experimental results on synthetic and real data show that both methods have promising performance.

We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized - which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to lI-SVM when the number of classes k 2. Both approaches are optimal in size of 21 where I is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.

We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We interpret the matrix elements as being produced by an unknown kernel which operates on object pairs and we show that - under mild assumptions - these kernels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classifier which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not positive definite, and not even symmetric or square.

We present an algorithm to extract features from high-dimensional gene expression profiles, based on the knowledge of a graph which links together genes known to participate to successive reactions in metabolic pathways. Motivated by the intuition that biologically relevant features are likely to exhibit smoothness with respect to the graph topology, the algorithm involves encoding the graph and the set of expression profiles into kernel functions, and performing a generalized form of canonical correlation analysis in the corresponding reproducible kernel Hilbert spaces. Function prediction experiments for the genes of the yeast S. Cerevisiae validate this approach by showing a consistent increase in performance when a state-of-the-art classifier uses the vector of features instead of the original expression profile to predict the functional class of a gene.

We introduce a family of classifiers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classifiers, includes the two best-known support-vector machines (SVMs), the ν-SVM and the C-SVM. In the electrostatics analogy, a training example corresponds to a charged conductor at a given location in space, the classification function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algorithms and their interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-definite kernels, regularization techniques that allow for the construction of an optimal classifier in Minkowski space. Based on the framework, we propose novel SVMs and perform simulation studies to show that they are comparable or superior to standard SVMs. The experiments include classification tasks on data which are represented in terms of their pairwise proximities, where a Coulomb Classifier outperformed standard SVMs.