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 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.

The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body models. To cope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphical model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is impractical and the random variables in our model must be continuousvalued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter. This framework facilitates the automatic initialization of the body-model from low level cues and is robust to occlusion of body parts and scene clutter.

We address in this paper the question of how the knowledge of the marginal distribution P (x) can be incorporated in a learning algorithm. We suggest three theoretical methods for taking into account this distribution for regularization and provide links to existing graph-based semi-supervised learning algorithms. We also propose practical implementations.

The problem of "Structure From Motion" is a central problem in vision: given the 2D locations of certain points we wish to recover the camera motion and the 3D coordinates of the points. Under simplified camera models, the problem reduces to factorizing a measurement matrix into the product of two low rank matrices. Each element of the measurement matrix contains the position of a point in a particular image. When all elements are observed, the problem can be solved trivially using SVD, but in any realistic situation many elements of the matrix are missing and the ones that are observed have a different directional uncertainty. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this paper we use the well known EM algorithm for factor analysis to perform factorization. This allows us to easily handle missing data and measurement uncertainty and more importantly allows us to place a prior on the temporal trajectory of the latent variables (the camera position). We show that incorporating this prior gives a significant improvement in performance in challenging image sequences.

We present an analysis of concentration-of-expectation phenomena in layered Bayesian networks that use generalized linear models as the local conditional probabilities. This framework encompasses a wide variety of probability distributions, including both discrete and continuous random variables. We utilize ideas from large deviation analysis and the delta method to devise and evaluate a class of approximate inference algorithms for layered Bayesian networks that have superior asymptotic error bounds and very fast computation time.

We present the software architecture of a robotic system for mapping abandoned mines. The software is capable of acquiring consistent 2D maps of large mines with many cycles, represented as Markov random £elds.

The maximisation of information transmission over noisy channels is a common, albeit generally computationally difficult problem. We approach the difficulty of computing the mutual information for noisy channels by using a variational approximation. The resulting IM algorithm is analagous to the EM algorithm, yet maximises mutual information, as opposed to likelihood. We apply the method to several practical examples, including linear compression, population encoding and CDMA.

We address in this paper the question of how the knowledge of the marginal distribution P (x) can be incorporated in a learning algorithm. We suggest three theoretical methods for taking into account this distribution for regularization and provide links to existing graph-based semi-supervised learning algorithms. We also propose practical implementations.

We propose an approach to learning the semantics of images which allows us to automatically annotate an image with keywords and to retrieve images based on text queries. We do this using a formalism that models the generation of annotated images. We assume that every image is divided into regions, each described by a continuous-valued feature vector. Given a training set of images with annotations, we compute a joint probabilistic model of image features and words which allow us to predict the probability of generating a word given the image regions. This may be used to automatically annotate and retrieve images given a word as a query. Experiments show that our model significantly outperforms the best of the previously reported results on the tasks of automatic image annotation and retrieval.