We apply the spike-and-slab Restricted Boltzmann Machine (ssRBM) to texture modeling. The ssRBM with tiled-convolution weight sharing (TssRBM) achieves or surpasses the state-of-the-art on texture synthesis and inpainting by parametric models. We also develop a novel RBM model with a spike-and-slab visible layer and binary variables in the hidden layer. This model is designed to be stacked on top of the TssRBM. We show the resulting deep belief network (DBN) is a powerful generative model that improves on single-layer models and is capable of modeling not only single high-resolution and challenging textures but also multiple textures.

A basic assumption of statistical learning theory is that train and test data are drawn from the same underlying distribution. Unfortunately, this assumption doesn't hold in many applications. Instead, ample labeled data might exist in a particular `source' domain while inference is needed in another, `target' domain. Domain adaptation methods leverage labeled data from both domains to improve classification on unseen data in the target domain. In this work we survey domain transfer learning methods for various application domains with focus on recent work in Computer Vision.

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariate-dependent latent feature model and topic model that obtain superior predictive performance.

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods for the traveling salesman problem. This ordering significantly reduces the search space for the subsequent greedy optimization that computes the final structure of the Bayesian network. We demonstrate our approach of learning Bayesian networks on real world census and weather datasets. In both cases, we demonstrate that the approach very accurately captures dependencies between random variables. We check the accuracy of the predictions based on independent studies in both application domains.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We develop a time-varying extension of our model, and apply it to the New York Times lists of weekly bestselling books.

Decision tree is an effective classification approach in data mining and machine learning. In applications, test costs and misclassification costs should be considered while inducing decision trees. Recently, some cost-sensitive learning algorithms based on ID3 such as CS-ID3, IDX, \lambda-ID3 have been proposed to deal with the issue. These algorithms deal with only symbolic data. In this paper, we develop a decision tree algorithm inspired by C4.5 for numeric data. There are two major issues for our algorithm. First, we develop the test cost weighted information gain ratio as the heuristic information. According to this heuristic information, our algorithm is to pick the attribute that provides more gain ratio and costs less for each selection. Second, we design a post-pruning strategy through considering the tradeoff between test costs and misclassification costs of the generated decision tree. In this way, the total cost is reduced. Experimental results indicate that (1) our algorithm is stable and effective; (2) the post-pruning technique reduces the total cost significantly; (3) the competition strategy is effective to obtain a cost-sensitive decision tree with low cost.

Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with Gaussian covariates and responses. In this paper, we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models. We show that the proposed methods, with Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] as a very special case, also possess the sure screening property with vanishing false selection rate. The conditions under which the independence learning possesses a sure screening is surprisingly simple. This justifies the applicability of such a simple method in a wide spectrum. We quantify explicitly the extent to which the dimensionality can be reduced by independence screening, which depends on the interactions of the covariance matrix of covariates and true parameters. Simulation studies are used to illustrate the utility of the proposed approaches. In addition, we establish an exponential inequality for the quasi-maximum likelihood estimator which is useful for high-dimensional statistical learning.

Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model are estimated conditional on that graph structure. While the probability distributions involved in this second step have been studied in depth, the ones used in the first step have not been explored in as much detail. In this paper, we will study the prior and posterior distributions defined over the space of the graph structures for the purpose of learning the structure of a graphical model. In particular, we will provide a characterisation of the behaviour of those distributions as a function of the possible edges of the graph. We will then use the properties resulting from this characterisation to define measures of structural variability for both Bayesian and Markov networks, and we will point out some of their possible applications.

We describe an inference task in which a set of timestamped event observations must be clustered into an unknown number of temporal sequences with independent and varying rates of observations. Various existing approaches to multi-object tracking assume a fixed number of sources and/or a fixed observation rate; we develop an approach to inferring structure in timestamped data produced by a mixture of an unknown and varying number of similar Markov renewal processes, plus independent clutter noise. The inference simultaneously distinguishes signal from noise as well as clustering signal observations into separate source streams. We illustrate the technique via a synthetic experiment as well as an experiment to track a mixture of singing birds.