We prove certain theoretical properties of a graph-regularized transductive learning objective that is based on minimizing a Kullback-Leibler divergence based loss. These include showing that the iterative alternating minimization procedure used to minimize the objective converges to the correct solution and deriving a test for convergence. We also propose a graph node ordering algorithm that is cache cognizant and leads to a linear speedup in parallel computations. This ensures that the algorithm scales to large data sets. By making use of empirical evaluation on the TIMIT and Switchboard I corpora, we show this approach is able to out-perform other state-of-the-art SSL approaches. In one instance, we solve a problem on a 120 million node graph.

Principal component analysis is a fundamental operation in computational data analysis, with myriad applications ranging from web search to bioinformatics to computer vision and image analysis. However, its performance and applicability in real scenarios are limited by a lack of robustness to outlying or corrupted observations. Thispaper considers the idealized "robust principal component analysis" problem of recovering a low rank matrix A from corrupted observations D A E. Here, the corrupted entries E are unknown and the errors can be arbitrarily large (modeling grossly corrupted observations common in visual and bioinformatic data), but are assumed to be sparse. We prove that most matrices A can be efficiently and exactly recovered from most error sign-and-support patterns bysolving a simple convex program, for which we give a fast and provably convergent algorithm. Our result holds even when the rank of A grows nearly proportionally (up to a logarithmic factor) to the dimensionality of the observation spaceand the number of errors E grows in proportion to the total number of entries in the matrix. A byproduct of our analysis is the first proportional growth results for the related problem of completing a low-rank matrix from a small fraction ofits entries. Simulations and real-data examples corroborate the theoretical results, and suggest potential applications in computer vision.

We describe a primal-dual framework for the design and analysis of online strongly convex optimization algorithms. Our framework yields the tightest known logarithmic regret bounds for Follow-The-Leader and for the gradient descent algorithm proposed in HazanKaKaAg06. We then show that one can interpolate between these two extreme cases. In particular, we derive a new algorithm that shares the computational simplicity of gradient descent but achieves lower regret in many practical situations. Finally, we further extend our framework for generalized strongly convex functions.

We introduce a framework for actively learning visual categories from a mixture of weakly and strongly labeled image examples. We propose to allow the category-learner to strategically choose what annotations it receives---based on both the expected reduction in uncertainty as well as the relative costs of obtaining each annotation. We construct a multiple-instance discriminative classifier based on the initial training data. Then all remaining unlabeled and weakly labeled examples are surveyed to actively determine which annotation ought to be requested next. After each request, the current classifier is incrementally updated. Unlike previous work, our approach accounts for the fact that the optimal use of manual annotation may call for a combination of labels at multiple levels of granularity (e.g., a full segmentation on some images and a present/absent flag on others). As a result, it is possible to learn more accurate category models with a lower total expenditure of manual annotation effort.

By attempting to simultaneously partition both the rows (examples) and columns (features) of a data matrix, Co-clustering algorithms often demonstrate surpris- ingly impressive performance improvements over traditional one-sided (row) clustering techniques. A good clustering of features may be seen as a combinatorial transformation of the data matrix, effectively enforcing a form of regularization that may lead to a better clustering of examples (and vice-versa). In many applications, partial supervision in the form of a few row labels as well as column labels may be available to potentially assist co-clustering. In this paper, we develop two novel semi-supervised multi-class classification algorithms motivated respectively by spectral bipartite graph partitioning and matrix approximation (e.g., non-negative matrix factorization) formulations for co-clustering. These algorithms (i) support dual supervision in the form of labels for both examples and/or features, (ii) provide principled predictive capability on out-of-sample test data, and (iii) arise naturally from the classical Representer theorem applied to regularization problems posed on a collection of Reproducing Kernel Hilbert Spaces. Empirical results demonstrate the effectiveness and utility of our algorithms.

In the quest to make Brain Computer Interfacing (BCI) more usable, dry electrodes have emerged that get rid of the initial 30 minutes required for placing an electrode cap. Another time consuming step is the required individualized adaptation to the BCI user, which involves another 30 minutes calibration for assessing a subjects brain signature. In this paper we aim to also remove this calibration proceedure from BCI setup time by means of machine learning. In particular, we harvest a large database of EEG BCI motor imagination recordings (83 subjects) for constructing a library of subject-specific spatio-temporal filters and derive a subject independent BCI classifier. Our offline results indicate that BCI-na\{i}ve users could start real-time BCI use with no prior calibration at only a very moderate performance loss."

We present a new family of linear time algorithms based on sufficient statistics for string comparison with mismatches under the string kernels framework. Our algorithms improve theoretical complexity bounds of existing approaches while scaling well with respect to the sequence alphabet size, the number of allowed mismatches and the size of the dataset. In particular, on large alphabets with loose mismatch constraints our algorithms are several orders of magnitude faster than the existing algorithms for string comparison under the mismatch similarity measure. We evaluate our algorithms on synthetic data and real applications in music genre classification, protein remote homology detection and protein fold prediction. The scalability of the algorithms allows us to consider complex sequence transformations, modeled using longer string features and larger numbers of mismatches, leading to a state-of-the-art performance with significantly reduced running times.

We describe, analyze, and experiment with a new framework for empirical loss minimization with regularization. Our algorithmic framework alternates between two phases. On each iteration we first perform an {\em unconstrained} gradient descent step. We then cast and solve an instantaneous optimization problem that trades off minimization of a regularization term while keeping close proximity to the result of the first phase. This yields a simple yet effective algorithm for both batch penalized risk minimization and online learning. Furthermore, the two phase approach enables sparse solutions when used in conjunction with regularization functions that promote sparsity, such as $\ell_1$. We derive concrete and very simple algorithms for minimization of loss functions with $\ell_1$, $\ell_2$, $\ell_2^2$, and $\ell_\infty$ regularization. We also show how to construct efficient algorithms for mixed-norm $\ell_1/\ell_q$ regularization. We further extend the algorithms and give efficient implementations for very high-dimensional data with sparsity. We demonstrate the potential of the proposed framework in experiments with synthetic and natural datasets.

We propose new methodologies to detect anomalies in discrete-time processes taking values in a probability space. These methods are based on the inference of functionals whose evaluations on successive states visited by the process are stationary and have low autocorrelations. Deviations from this behavior are used to flag anomalies. The candidate functionals are estimated in a subspace of a reproducing kernel Hilbert space associated with the original probability space considered. We provide experimental results on simulated datasets which show that these techniques compare favorably with other algorithms.

We introduce a kernel-based method for change-point analysis within a sequence of temporal observations. Change-point analysis of an (unlabelled) sample of observations consists in, first, testing whether a change in the distribution occurs within the sample, and second, if a change occurs, estimating the change-point instant after which the distribution of the observations switches from one distribution to another different distribution. We propose a test statistics based upon the maximum kernel Fisher discriminant ratio as a measure of homogeneity between segments. We derive its limiting distribution under the null hypothesis (no change occurs), and establish the consistency under the alternative hypothesis (a change occurs). This allows to build a statistical hypothesis testing procedure for testing the presence of change-point, with a prescribed false-alarm probability and detection probability tending to one in the large-sample setting. If a change actually occurs, the test statistics also yields an estimator of the change-point location. Promising experimental results in temporal segmentation of mental tasks from BCI data and pop song indexation are presented.