Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that is guaranteed to be fast mixing, under several divergences. We find that Gibbs sampling using the projected parameters is more accurate than with the original parameters when interaction strengths are strong and when limited time is available for sampling.

In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T,n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, which constitutes the solution to the tracking problem, as well as the model parameters. In the numerical section, we present performance comparisons with several competing techniques and demonstrate significant performance improvements in all cases.

Measuring the effectiveness of corporate environmental reports, it being highly qualitative and less regulated, is often considered as a daunting task. The task becomes more complex if comparisons are to be performed. This study is undertaken to overcome the physical verification problems by implementing data mining technique. It further explores on the effectiveness by performing exploratory analysis and structural equation model to bring out the significant linkages between the selected 10 variables. Samples of five hundred and thirty nine reports across various countries are used from an international directory to perform the statistical analysis like: One way ANOVA (Analysis of Variance), MDA (Multivariate Discriminant Analysis) and SEM (Structural Equation Modeling). The results indicate the significant differences among the various types of industries in their environmental reporting, and the exploratory factors like stakeholder, organization strategy and industrial oriented factors, proved significant. The major accomplishment is that the findings correlate with the conceptual frame work of GRI.

In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowledge, the first leading to linear and polygonal constraints on the hypothesis space, the second leading to quadratic constraints, and the last leading to conic constraints. We show how different types of domain knowledge can lead directly to these kinds of side knowledge. We prove bounds on complexity measures of the hypothesis space for quadratic and conic side knowledge, and show that these bounds are tight in a specific sense for the quadratic case.

Many classification problems can be difficult to formulate directly in terms of the traditional supervised setting, where both training and test samples are individual feature vectors. There are cases in which samples are better described by sets of feature vectors, that labels are only available for sets rather than individual samples, or, if individual labels are available, that these are not independent. To better deal with such problems, several extensions of supervised learning have been proposed, where either training and/or test objects are sets of feature vectors. However, having been proposed rather independently of each other, their mutual similarities and differences have hitherto not been mapped out. In this work, we provide an overview of such learning scenarios, propose a taxonomy to illustrate the relationships between them, and discuss directions for further research in these areas.

Bipartite ranking aims to learn a real-valued ranking function that orders positive instances before negative instances. Recent efforts of bipartite ranking are focused on optimizing ranking accuracy at the top of the ranked list. Most existing approaches are either to optimize task specific metrics or to extend the ranking loss by emphasizing more on the error associated with the top ranked instances, leading to a high computational cost that is super-linear in the number of training instances. We propose a highly efficient approach, titled TopPush, for optimizing accuracy at the top that has computational complexity linear in the number of training instances. We present a novel analysis that bounds the generalization error for the top ranked instances for the proposed approach. Empirical study shows that the proposed approach is highly competitive to the state-of-the-art approaches and is 10-100 times faster.

While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based methods, which limits their scalability. In this paper, we present a variational inference framework for models involving gamma process priors. Our approach is based on a novel stick-breaking constructive definition of the gamma process. We prove correctness of this stick-breaking process by using the characterization of the gamma process as a completely random measure (CRM), and we explicitly derive the rate measure of our construction using Poisson process machinery. We also derive error bounds on the truncation of the infinite process required for variational inference, similar to the truncation analyses for other nonparametric models based on the Dirichlet and beta processes. Our representation is then used to derive a variational inference algorithm for a particular Bayesian nonparametric latent structure formulation known as the infinite Gamma-Poisson model, where the latent variables are drawn from a gamma process prior with Poisson likelihoods. Finally, we present results for our algorithms on nonnegative matrix factorization tasks on document corpora, and show that we compare favorably to both sampling-based techniques and variational approaches based on beta-Bernoulli priors.

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at single cell level and geometric processing by means of cells connectivity. We present a geometric model of such connectivities in the space of detected features associated to spatio-temporal visual stimuli, and show how they can be used to obtain low-level object segmentation. The main idea is that of defining a spectral clustering procedure with anisotropic affinities over datasets consisting of embeddings of the visual stimuli into higher dimensional spaces. Neural plausibility of the proposed arguments will be discussed.

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and makes no assumptions regarding data normalization. The prediction speed of approximated models no longer relates to the amount of support vectors but is quadratic in terms of the number of input dimensions. If the number of input dimensions is small compared to the amount of support vectors, the approximated model is significantly faster in prediction and has a smaller memory footprint. An optimized C++ implementation was made to assess the gain in prediction speed in a set of practical tests. We additionally provide a method to verify the approximation accuracy, prior to training models or during run-time, to ensure the loss in accuracy remains acceptable and within known bounds.