A dynamic texture is a video model that treats a video as a sample from a spatiotemporal stochastic process, specifically a linear dynamical system. One problem associated with the dynamic texture is that it cannot model video where there are multiple regions of distinct motion. In this work, we introduce the layered dynamic texture model, which addresses this problem. We also introduce a variant of the model, and present the EM algorithm for learning each of the models. Finally, we demonstrate the efficacy of the proposed model for the tasks of segmentation and synthesis of video.

We present a new kernel method for extracting semantic relations between entities in natural language text, based on a generalization of subsequence kernels. This kernel uses three types of subsequence patterns that are typically employed in natural language to assert relationships between two entities. Experiments on extracting protein interactions from biomedical corpora and top-level relations from newspaper corpora demonstrate the advantages of this approach.

We present an efficient algorithm to actively select queries for learning the boundaries separating a function domain into regions where the function is above and below a given threshold. We develop experiment selection methods based on entropy, misclassification rate, variance, and their combinations, and show how they perform on a number of data sets. We then show how these algorithms are used to determine simultaneously valid 1 α confidence intervals for seven cosmological parameters. Experimentation shows that the algorithm reduces the computation necessary for the parameter estimation problem by an order of magnitude.

A model of bottom-up overt attention is proposed based on the principle of maximizing information sampled from a scene. The proposed operation is based on Shannon's self-information measure and is achieved in a neural circuit, which is demonstrated as having close ties with the circuitry existent in the primate visual cortex. It is further shown that the proposed saliency measure may be extended to address issues that currently elude explanation in the domain of saliency based models. Results on natural images are compared with experimental eye tracking data revealing the efficacy of the model in predicting the deployment of overt attention as compared with existing efforts. 1 Introduction There has long been interest in the nature of eye movements and fixation behavior following early studies by Buswell [I] and Yarbus [2]. However, a complete description of the mechanisms underlying these peculiar fixation patterns remains elusive.

Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than x-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [1]. We derive a mean-field variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. The CTM gives a better fit than LDA on a collection of OCRed articles from the journal Science. Furthermore, the CTM provides a natural way of visualizing and exploring this and other unstructured data sets.

This paper proposes an algorithm to convert a T -stage stochastic decision problem with a continuous state space to a sequence of supervised learning problems. The optimization problem associated with the trajectory tree and random trajectory methods of Kearns, Mansour, and Ng, 2000, is solved using the Gauss-Seidel method. The algorithm breaks a multistage reinforcement learning problem into a sequence of single-stage reinforcement learning subproblems, each of which is solved via an exact reduction to a weighted-classification problem that can be solved using off-the-self methods. Thus the algorithm converts a reinforcement learning problem into simpler supervised learning subproblems. It is shown that the method converges in a finite number of steps to a solution that cannot be further improved by componentwise optimization. The implication of the proposed algorithm is that a plethora of classification methods can be applied to find policies in the reinforcement learning problem.

We propose a new linear method for dimension reduction to identify non-Gaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. Once NGCA components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.

Convexity has recently received a lot of attention in the machine learning community, and the lack of convexity has been seen as a major disadvantage of many learning algorithms, such as multi-layer artificial neural networks. We show that training multi-layer neural networks in which the number of hidden units is learned can be viewed as a convex optimization problem. This problem involves an infinite number of variables, but can be solved by incrementally inserting a hidden unit at a time, each time finding a linear classifier that minimizes a weighted sum of errors.

To escape from the curse of dimensionality, we claim that one can learn non-local functions, in the sense that the value and shape of the learned function at x must be inferred using examples that may be far from x. With this objective, we present a non-local nonparametric density estimator. It builds upon previously proposed Gaussian mixture models with regularized covariance matrices to take into account the local shape of the manifold. It also builds upon recent work on non-local estimators of the tangent plane of a manifold, which are able to generalize in places with little training data, unlike traditional, local, nonparametric models.

We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smoothness prior - with similarity between examples expressed with a local kernel - are sensitive to the curse of dimensionality, or more precisely to the variability of the target. Our discussion covers supervised, semisupervised and unsupervised learning algorithms. These algorithms are found to be local in the sense that crucial properties of the learned function at x depend mostly on the neighbors of x in the training set. This makes them sensitive to the curse of dimensionality, well studied for classical nonparametric statistical learning. We show in the case of the Gaussian kernel that when the function to be learned has many variations, these algorithms require a number of training examples proportional to the number of variations, which could be large even though there may exist short descriptions of the target function, i.e. their Kolmogorov complexity may be low. This suggests that there exist non-local learning algorithms that at least have the potential to learn about such structured but apparently complex functions (because locally they have many variations), while not using very specific prior domain knowledge.