We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset.

This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1 133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs.

We propose a simple kernel based nearest neighbor approach for handwritten digit classification. The "distance" here is actually a kernel defining the similarity between two images. We carefully study the effects of different number of neighbors and weight schemes and report the results. With only a few nearest neighbors (or most similar images) to vote, the test set error rate on MNIST database could reach about 1.5%-2.0%, which is very close to many advanced models.

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering a more accurate way to deal with finite sample issues. We derive a bound minimization algorithm and show that it provides good results in real-life problems and that the derived PAC-Bayesian bound is reasonably tight.

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits multiple modalities, such as acoustic and visual content of video. Integrating such heterogeneous data to form a holistic similarity space is therefore a key challenge to be overcome in many real-world applications. We present a novel multiple kernel learning technique for integrating heterogeneous data into a single, unified similarity space. Our algorithm learns an optimal ensemble of kernel transfor- mations which conform to measurements of human perceptual similarity, as expressed by relative comparisons. To cope with the ubiquitous problems of subjectivity and inconsistency in multi- media similarity, we develop graph-based techniques to filter similarity measurements, resulting in a simplified and robust training procedure.

The Aviation Safety Reporting System collects voluntarily submitted reports on aviation safety incidents to facilitate research work aiming to reduce such incidents. To effectively reduce these incidents, it is vital to accurately identify why these incidents occurred. More precisely, given a set of possible causes, or shaping factors, this task of cause identification involves identifying all and only those shaping factors that are responsible for the incidents described in a report. We investigate two approaches to cause identification. Both approaches exploit information provided by a semantic lexicon, which is automatically constructed via Thelen and Riloff's Basilisk framework augmented with our linguistic and algorithmic modifications. The first approach labels a report using a simple heuristic, which looks for the words and phrases acquired during the semantic lexicon learning process in the report. The second approach recasts cause identification as a text classification problem, employing supervised and transductive text classification algorithms to learn models from incident reports labeled with shaping factors and using the models to label unseen reports. Our experiments show that both the heuristic-based approach and the learning-based approach (when given sufficient training data) outperform the baseline system significantly.

Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus, we present NESVM, a fast gradient SVM solver that can optimize various SVM models, e.g., classical SVM, linear programming SVM and least square SVM. Compared against SVM-Perf \cite{SVM_Perf}\cite{PerfML} (its convergence rate in solving the dual SVM is upper bounded by $\mathcal O(1/\sqrt{k})$, wherein $k$ is the number of iterations.) and Pegasos \cite{Pegasos} (online SVM that converges at rate $\mathcal O(1/k)$ for the primal SVM), NESVM achieves the optimal convergence rate at $\mathcal O(1/k^{2})$ and a linear time complexity. In particular, NESVM smoothes the non-differentiable hinge loss and $\ell_1$-norm in the primal SVM. Then the optimal gradient method without any line search is adopted to solve the optimization. In each iteration round, the current gradient and historical gradients are combined to determine the descent direction, while the Lipschitz constant determines the step size. Only two matrix-vector multiplications are required in each iteration round. Therefore, NESVM is more efficient than existing SVM solvers. In addition, NESVM is available for both linear and nonlinear kernels. We also propose "homotopy NESVM" to accelerate NESVM by dynamically decreasing the smooth parameter and using the continuation method. Our experiments on census income categorization, indoor/outdoor scene classification, event recognition and scene recognition suggest the efficiency and the effectiveness of NESVM. The MATLAB code of NESVM will be available on our website for further assessment.

Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance index (C index) [Harrell et al. (1982)]. The C-index can be interpreted as a misclassification probability and does not depend on a single fixed time for evaluation. The C-index also specifically accounts for censoring. By utilizing kernel functions, KIRSF achieves better results than RSF in many situations. In this report, we show how to incorporate kernel functions into RSF. We test the performance of KIRSF and compare our method to RSF. We find that the KIRSF's performance is better than RSF in many occasions.

Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and generalized ultrametric in logic. In particular we study approximation chains in an ultrametric or generalized ultrametric context. Our aim in this work is to extend the scope of data analysis by facilitating reasoning based on the data analysis; and to show how quantitative and qualitative data analysis can be incorporated into logic programming.