We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed random variables, and study its statistical properties. We consider applications to topic modeling and derive a variational inference algorithm for approximate posterior inference. We study the empirical performance of the DILN topic model on four corpora, comparing performance with the HDP and the correlated topic model (CTM). To deal with large-scale data sets, we also develop an online inference algorithm for DILN and compare with online HDP and online LDA on the Nature magazine, which contains approximately 350,000 articles.

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace scale mixtures can subserve a Bayesian framework for sparse learning with nonconvex penalization. The densities of EP-GIG can be explicitly expressed. Moreover, the corresponding posterior distribution also follows a generalized inverse Gaussian distribution. These properties lead us to EM algorithms for Bayesian sparse learning. We show that these algorithms bear an interesting resemblance to iteratively re-weighted $\ell_2$ or $\ell_1$ methods. In addition, we present two extensions for grouped variable selection and logistic regression.

Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors should this training data be systematically inaccurate for example due to the assumed MC model. To complement such model-dependent searches, we propose an algorithm based on semi-supervised anomaly detection techniques, which does not require a MC training sample for the signal data. We first model the background using a multivariate Gaussian mixture model. We then search for deviations from this model by fitting to the observations a mixture of the background model and a number of additional Gaussians. This allows us to perform pattern recognition of any anomalous excess over the background. We show by a comparison to neural network classifiers that such an approach is a lot more robust against misspecification of the signal MC than supervised classification. In cases where there is an unexpected signal, a neural network might fail to correctly identify it, while anomaly detection does not suffer from such a limitation. On the other hand, when there are no systematic errors in the training data, both methods perform comparably.

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.

We present a framework that allows an observer to determine occluded portions of a structure by finding the maximum-likelihood estimate of those occluded portions consistent with visible image evidence and a consistency model. Doing this requires determining which portions of the structure are occluded in the first place. Since each process relies on the other, we determine a solution to both problems in tandem. We extend our framework to determine confidence of one's assessment of which portions of an observed structure are occluded, and the estimate of that occluded structure, by determining the sensitivity of one's assessment to potential new observations. We further extend our framework to determine a robotic action whose execution would allow a new observation that would maximally increase one's confidence.

This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and reveal the impact of various relation types on performance quality. For that, we define the overall relations between object pairs as a \textit{link pattern} which consists in interaction pattern and connection structure in the network, and then use tensor formalization to jointly model and predict the link patterns, which we refer to as \textit{Link Pattern Prediction} (LPP) problem. To address the issue, we propose a Probabilistic Latent Tensor Factorization (PLTF) model by introducing another latent factor for multiple relation types and furnish the Hierarchical Bayesian treatment of the proposed probabilistic model to avoid overfitting for solving the LPP problem. To learn the proposed model we develop an efficient Markov Chain Monte Carlo sampling method. Extensive experiments are conducted on several real world datasets and demonstrate significant improvements over several existing state-of-the-art methods.

In information retrieval, a fundamental goal is to transform a document into concepts that are representative of its content. The term "representative" is in itself challenging to define, and various tasks require different granularities of concepts. In this paper, we aim to model concepts that are sparse over the vocabulary, and that flexibly adapt their content based on other relevant semantic information such as textual structure or associated image features. We explore a Bayesian nonparametric model based on nested beta processes that allows for inferring an unknown number of strictly sparse concepts. The resulting model provides an inherently different representation of concepts than a standard LDA (or HDP) based topic model, and allows for direct incorporation of semantic features. We demonstrate the utility of this representation on multilingual blog data and the Congressional Record.

ABSTRACT On dedicated websites, people can upload videos and share it with the rest of the world. Currently these videos are categorized manually by the help of the user community. In this paper, we propose a combination of color spaces with the Bayesian network approach for robust detection of skin color followed by an automated video categorization. Experimental results show that our method can achieve satisfactory performance for categorizing videos based on skin color. Keywords: video categorization, skin detection in videos, color spaces 1. INTRODUCTION Locating and tracking patches of skin-colored pixels through an image is a tool used in many face recognition and gesture tracking systems [13][8].

Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algorithms. In order to limit the search space and escape from local maxima produced by executing EM algorithm, this paper presents a learning parameter algorithm that is a fusion of EM and RBE algorithms. This algorithm incorporates the range of a parameter into the EM algorithm. This range is calculated by the first step of RBE algorithm allowing a regularization of each parameter in bayesian network after the maximization step of the EM algorithm. The threshold EM algorithm is applied in brain tumor diagnosis and show some advantages and disadvantages over the EM algorithm.