Online learning algorithms have impressive convergence properties when it comes to risk minimization and convex games on very large problems. However, they are inherently sequential in their design which prevents them from taking advantage of modern multi-core architectures. In this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.

Spectral clustering is useful for a wide-ranging set of applications in areas such as biological data analysis, image processing and data mining. However, the computational and/or communication resources required by the method in processing large-scale data sets are often prohibitively high, and practitioners are often required to perturb the original data in various ways (quantization, downsampling, etc) before invoking a spectral algorithm. In this paper, we use stochastic perturbation theory to study the effects of data perturbation on the performance of spectral clustering. We show that the error under perturbation of spectral clustering is closely related to the perturbation of the eigenvectors of the Laplacian matrix. From this result we derive approximate upper bounds on the clustering error. We show that this bound is tight empirically across a wide range of problems, suggesting that it can be used in practical settings to determine the amount of data reduction allowed in order to meet a specification of permitted loss in clustering performance.

We consider multi-label prediction problems with large output spaces under the assumption of output sparsity - that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than others. We also state and prove robustness guarantees for this method in the form of regret transform bounds (in general), and also provide a more detailed analysis for the linear prediction setting.

Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph. In this paper we investigate the influence of the construction of the similarity graph on the clustering results. We first study the convergence of graph clustering criteria such as the normalized cut (Ncut) as the sample size tends to infinity. We find that the limit expressions are different for different types of graph, for example the r-neighborhood graph or the k-nearest neighbor graph. In plain words: Ncut on a kNN graph does something systematically different than Ncut on an r-neighborhood graph! This finding shows that graph clustering criteria cannot be studied independently of the kind of graph they are applied to. We also provide examples which show that these differences can be observed for toy and real data already for rather small sample sizes.

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.

Neuroimaging datasets often have a very large number of voxels and a very small number of training cases, which means that overfitting of models for this data can become a very serious problem. Working with a set of fMRI images from a study on stroke recovery, we consider a classification task for which logistic regression performs poorly, even when L1-or L2-regularized. We show that much better discrimination can be achieved by fitting a generative model to each separate condition and then seeing which model is most likely to have generated the data. We compare discriminative training of exactly the same set of models, and we also consider convex blends of generative and discriminative training.

The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

In this article, we propose fast subtree kernels on graphs.

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.

CAPTCHAs are computer-generated tests that humans can pass but current computer systems cannot. CAPTCHAs provide a method for automatically distinguishing a human from a computer program, and therefore can protect Web services from abuse by so-called "bots." Most CAPTCHAs consist of distorted images, usually text, for which a user must provide some description. Unfortunately, visual CAPTCHAs limit access to the millions of visually impaired people using the Web. Audio CAPTCHAs were created to solve this accessibility issue; however, the security of audio CAPTCHAs was never formally tested.