A new algorithm for on-line learning linear-threshold functions is proposed which efficiently combines second-order statistics about the data with the logarithmic behavior" of multiplicative/dual-norm algorithms. An initial theoretical analysis is provided suggesting that our algorithm might be viewed as a standard Perceptron algorithm operating on a transformed sequence of examples with improved margin properties. We also report on experiments carried out on datasets from diverse domains, with the goal of comparing to known Perceptron algorithms (first-order, second-order, additive, multiplicative). Our learning procedure seems to generalize quite well, and converges faster than the corresponding multiplicative baseline algorithms."

Empirical risk minimization offers well-known learning guarantees when training and test data come from the same domain. In the real world, though, we often wish to adapt a classifier from a source domain with a large amount of training data to different target domain with very little training data. In this work we give uniform convergence bounds for algorithms that minimize a convex combination of source and target empirical risk. The bounds explicitly model the inherent trade-off between training on a large but inaccurate source data set and a small but accurate target training set. Our theory also gives results when we have multiple source domains, each of which may have a different number of instances, and we exhibit cases in which minimizing a non-uniform combination of source risks can achieve much lower target error than standard empirical risk minimization.

Statistical models on full and partial rankings of n items are often of limited practical usefor large n due to computational consideration. We explore the use of nonparametric models for partially ranked data and derive efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. In particular, we demonstrate for the first time a nonparametric coherent and consistent model capable of efficiently aggregating partially ranked data of different types.

When we have several related tasks, solving them simultaneously is shown to be more effective than solving them individually. This approach is called multi-task learning (MTL) and has been studied extensively. Existing approaches to MTL often treat all the tasks as \emph{uniformly related to each other and the relatedness of the tasks is controlled globally. For this reason, the existing methods can lead to undesired solutions when some tasks are not highly related to each other, and some pairs of related tasks can have significantly different solutions. In this paper, we propose a novel MTL algorithm that can overcome these problems. Our method makes use of a task network, which describes the relation structure among tasks. This allows us to deal with intricate relation structures in a systematic way. Furthermore, we control the relatedness of the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines (SVMs) and show that the optimization problem can be cast as a second order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated through simulations with protein super-family classification and ordinal regression problems.

We present a general boosting method extending functional gradient boosting to optimize complex loss functions that are encountered in many machine learning problems. Our approach is based on optimization of quadratic upper bounds of the loss functions which allows us to present a rigorous convergence analysis of the algorithm. More importantly, this general framework enables us to use a standard regression base learner such as single regression tree for £tting any loss function. We illustrate an application of the proposed method in learning ranking functions for Web search by combining both preference data and labeled data for training. We present experimental results for Web search using data from a commercial search engine that show signi£cant improvements of our proposed methods over some existing methods.

Over the past few years, the notion of stability in data clustering has received growing attention as a cluster validation criterion in a sample-based framework. However, recent work has shown that as the sample size increases, any clustering model will usually become asymptotically stable. This led to the conclusion that stability is lacking as a theoretical and practical tool. The discrepancy between this conclusion and the success of stability in practice has remained an open question, whichwe attempt to address. Our theoretical approach is that stability, as used by cluster validation algorithms, is similar in certain respects to measures of generalization in a model-selection framework. In such cases, the model chosen governsthe convergence rate of generalization bounds. By arguing that these rates are more important than the sample size, we are led to the prediction that stability-based cluster validation algorithms should not degrade with increasing sample size, despite the asymptotic universal stability. This prediction is substantiated bya theoretical analysis as well as some empirical results. We conclude that stability remains a meaningful cluster validation criterion over finite samples.

We introduce a hierarchical Bayesian model for the discovery of putative regulators from gene expression data only. The hierarchy incorporates the knowledge that there are just a few regulators that by themselves only regulate a handful of genes. This is implemented through a so-called spike-and-slab prior, a mixture of Gaussians with different widths, with mixing weights from a hierarchical Bernoulli model. For efficient inference we implemented expectation propagation. Running the model on a malaria parasite data set, we found four genes with significant homology to transcription factors in an amoebe, one RNA regulator and three genes of unknown function (out of the top ten genes considered).

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.

We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over the state-of-the-art, and demonstrate our approach in document clustering and phylolinguistics.

Functional Magnetic Resonance Imaging (fMRI) provides an unprecedented window into the complex functioning of the human brain, typically detailing the activity of thousands of voxels during hundreds of sequential time points. Unfortunately, the interpretation of fMRI is complicated due both to the relatively unknown connection between the hemodynamic response and neural activity and the unknown spatiotemporal characteristics of the cognitive patterns themselves. Here, we use data from the Experience Based Cognition competition to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We build global low dimensional representations of an fMRI dataset, using linear and nonlinear methods. We learn a set of time series that are implicit functions of the fMRI data, and predict the values of these times series in the future from the knowledge of the fMRI data only. We find effective, low-dimensional models based on the principal components of cognitive activity in classically-defined anatomical regions, the Brodmann Areas. Furthermore for some of the stimuli, the top predictive regions were stable across subjects and episodes, including WernickeÕs area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions (Brodmann Area 7) for velocity. These interpretations and the relative simplicity of our approach provide a transparent and conceptual basis upon which to build more sophisticated techniques for fMRI decoding. To our knowledge, this is the first time that classical areas have been used in fMRI for an effective prediction of complex natural experience.