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.

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 are allowed. 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.

In this paper we present a generative latent variable model for rating-based collaborative filtering called the User Rating Profile model (URP). The generative process which underlies URP is designed to produce complete user rating profiles, an assignment of one rating to each item for each user. Our model represents each user as a mixture of user attitudes, and the mixing proportions are distributed according to a Dirichlet random variable. The rating for each item is generated by selecting a user attitude for the item, and then selecting a rating according to the preference pattern associated with that attitude. URP is related to several models including a multinomial mixture model, the aspect model [7], and LDA [1], but has clear advantages over each.

In real world planning problems, time for deliberation is often limited. Anytime planners are well suited for these problems: they find a feasible solution quickly and then continually work on improving it until time runs out. In this paper we propose an anytime heuristic search, ARA*, which tunes its performance bound based on available search time. It starts by finding a suboptimal solution quickly using a loose bound, then tightens the bound progressively as time allows. Given enough time it finds a provably optimal solution. While improving its bound, ARA* reuses previous search efforts and, as a result, is significantly more efficient than other anytime search methods. In addition to our theoretical analysis, we demonstrate the practical utility of ARA* with experiments on a simulated robot kinematic arm and a dynamic path planning problem for an outdoor rover.

We compute approximate analytical bootstrap averages for support vector classification using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of conditional probabilities in factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee Machine, and Gaussian Process chunking as special cases.

Biochemical signal-transduction networks are the biological information-processing systems by which individual cells, from neurons to amoebae, perceive and respond to their chemical environments. We introduce a simplified model of a single biochemical relay and analyse its capacity as a communications channel. A diffusible ligand is released by a sending cell and received by binding to a transmembrane receptor protein on a receiving cell. This receptor-ligand interaction creates a nonlinear communications channel with non-Gaussian noise. We model this channel numerically and study its response to input signals of different frequencies in order to estimate its channel capacity. Stochastic effects introduced in both the diffusion process and the receptor-ligand interaction give the channel low-pass characteristics. We estimate the channel capacity using a water-filling formula adapted from the additive white-noise Gaussian channel.

The area under an ROC curve (AUC) is a criterion used in many applications to measure the quality of a classification algorithm. However, the objective function optimized in most of these algorithms is the error rate and not the AUC value. We give a detailed statistical analysis of the relationship between the AUC and the error rate, including the first exact expression of the expected value and the variance of the AUC for a fixed error rate. Our results show that the average AUC is monotonically increasing as a function of the classification accuracy, but that the standard deviation for uneven distributions and higher error rates is noticeable. Thus, algorithms designed to minimize the error rate may not lead to the best possible AUC values. We show that, under certain conditions, the global function optimized by the RankBoost algorithm is exactly the AUC. We report the results of our experiments with RankBoost in several datasets demonstrating the benefits of an algorithm specifically designed to globally optimize the AUC over other existing algorithms optimizing an approximation of the AUC or only locally optimizing the AUC.

Principal components analysis (PCA) is one of the most widely used techniques in machine learning and data mining. Minor components analysis (MCA) is less well known, but can also play an important role in the presence of constraints on the data distribution. In this paper we present a probabilistic model for "extreme components analysis" (XCA) which at the maximum likelihood solution extracts an optimal combination of principal and minor components. For a given number of components, the log-likelihood of the XCA model is guaranteed to be larger or equal than that of the probabilistic models for PCA and MCA. We describe an efficient algorithm to solve for the globally optimal solution. For log-convex spectra we prove that the solution consists of principal components only, while for log-concave spectra the solution consists of minor components. In general, the solution admits a combination of both. In experiments we explore the properties of XCA on some synthetic and real-world datasets.

Given an N N grid of squares, where each square has a count and an underlying population, our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, can be used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D