In typical classification tasks, we seek a function which assigns a label to a single object. Kernel-based approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ability to use high-dimensional feature spaces, and from their strong theoretical guarantees. However, many real-world tasks involve sequential, spatial, or structured data, where multiple labels must be assigned. Existing kernel-based methods ignore structure in the problem, assigning labels independently to each object, losing much useful information. Conversely, probabilistic graphical models, such as Markov networks, can represent correlations between labels, by exploiting problem structure, but cannot handle high-dimensional feature spaces, and lack strong theoretical generalization guarantees.

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting--which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.

To provide a compact generative representation of the sequential activity of a number of individuals within a group there is a tradeoff between the definition of individual specific and global models. This paper proposes a linear-time distributed model for finite state symbolic sequences representing traces of individual user activity by making the assumption that heterogeneous user behavior may be'explained' by a relatively small number of common structurally simple behavioral patterns which may interleave randomly in a user-specific proportion. The results of an empirical study on three different sources of user traces indicates that this modelling approach provides an efficient representation scheme, reflected by improved prediction performance as well as providing lowcomplexity and intuitively interpretable representations.

The problem of approximating the product of several Gaussian mixture distributions arises in a number of contexts, including the nonparametric belief propagation (NBP) inference algorithm and the training of product of experts models. This paper develops two multiscale algorithms for sampling from a product of Gaussian mixtures, and compares their performance to existing methods. The first is a multiscale variant of previously proposed Monte Carlo techniques, with comparable theoretical guarantees but improved empirical convergence rates. The second makes use of approximate kernel density evaluation methods to construct a fast approximate sampler, which is guaranteed to sample points to within a tunable parameter ɛ of their true probability. We compare both multiscale samplers on a set of computational examples motivated by NBP, demonstrating significant improvements over existing methods.

In applying Hidden Markov Models to the analysis of massive data streams, it is often necessary to use an artificially reduced set of states; this is due in large part to the fact that the basic HMM estimation algorithms have a quadratic dependence on the size of the state set. We present algorithms that reduce this computational bottleneck to linear or near-linear time, when the states can be embedded in an underlying grid of parameters. This type of state representation arises in many domains; in particular, we show an application to traffic analysis at a high-volume Web site.

This paper presents an algorithm for learning the time-varying shape of a nonrigid 3D object from uncalibrated 2D tracking data. We model shape motion as a rigid component (rotation and translation) combined with a nonrigid deformation. Reconstruction is ill-posed if arbitrary deformations areallowed. We constrain the problem by assuming that the object shape at each time instant is drawn from a Gaussian distribution. Based on this assumption, the algorithm simultaneously estimates 3D shape and motion for each time frame, learns the parameters of the Gaussian, and robustly fills-in missing data points. We then extend the algorithm to model temporal smoothness in object shape, thus allowing it to handle severe cases of missing data.

Mutual Boosting is a method aimed at incorporating contextual information to augment object detection. When multiple detectors of objects and parts are trained in parallel using AdaBoost [1], object detectors might use the remaining intermediate detectors to enrich the weak learner set. This method generalizes the efficient features suggested by Viola and Jones [2] thus enabling information inference between parts and objects in a compositional hierarchy. In our experiments eye-, nose-, mouth-and face detectors are trained using the Mutual Boosting framework. Results show that the method outperforms applications overlooking contextual information. We suggest that achieving contextual integration is a step toward humanlike detection capabilities.

Standard approaches to object detection focus on local patches of the image, and try to classify them as background or not. We propose to use the scene context (image as a whole) as an extra source of (global) information, to help resolve local ambiguities. We present a conditional random field for jointly solving the tasks of object detection and scene classification.

Even under perfect fixation the human eye is under steady motion (tremor, microsaccades, slow drift). The "dynamic" theory of vision [1,2] states that eye-movements can improve hyperacuity. According to this theory, eye movements are thought to create variable spatial excitation patterns on the photoreceptor grid, which will allow for better spatiotemporal summation at later stages.

Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. Thismodel is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of maximum likelihoodestimation, and show that the computational problem of maximizing the likelihood is tractable.