Semi-supervised learning, i.e. learning from both labeled and unlabeled data has received significant attention in the machine learning literature in recent years. Still our understanding of the theoretical foundations of the usefulness of unlabeled data remains somewhat limited. The simplest and the best understood situation is when the data is described by an identifiable mixture model, and where each class comes from a pure component. This natural setup and its implications ware analyzed in [11, 5]. One important result was that in certain regimes, labeled data becomes exponentially more valuable than unlabeled data. However, in most realistic situations, one would not expect that the data comes from a parametric mixture distribution with identifiable components.

We consider the ensemble clustering problem where the task is to'aggregate' multiple clustering solutions into a single consolidated clustering that maximizes the shared information among given clustering solutions. We obtain several new results for this problem. First, we note that the notion of agreement under such circumstances can be better captured using an agreement measure based on a 2D string encoding rather than voting strategy based methods proposed in literature. Using this generalization, we first derive a nonlinear optimization model to maximize the new agreement measure. We then show that our optimization problem can be transformed into a strict 0-1 Semidefinite Program (SDP) via novel convexification techniques which can subsequently be relaxed to a polynomial time solvable SDP. Our experiments indicate improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. We discuss evaluations on clustering and image segmentation databases.

When predicting class labels for objects within a relational database, it is often helpful to consider a model for relationships: this allows for information between class labels to be shared and to improve prediction performance. However, there are different ways by which objects can be related within a relational database. One traditional way corresponds to a Markov network structure: each existing relation is represented by an undirected edge. This encodes that, conditioned on input features, each object label is independent of other object labels given its neighbors in the graph. However, there is no reason why Markov networks should be the only representation of choice for symmetric dependence structures. Here we discuss the case when relationships are postulated to exist due to hidden common causes. We discuss how the resulting graphical model differs from Markov networks, and how it describes different types of real-world relational processes. A Bayesian nonparametric classification model is built upon this graphical representation and evaluated with several empirical studies.

Estimation of three-dimensional articulated human pose and motion from images is a central problem in computer vision. Much of the previous work has been limited by the use of crude generative models of humans represented as articulated collections of simple parts such as cylinders. Automatic initialization of such models has proved difficult and most approaches assume that the size and shape of the body parts are known a priori. In this paper we propose a method for automatically recovering a detailed parametric model of nonrigid body shape and pose from monocular imagery. Specifically, we represent the body using a param-eterized triangulated mesh model that is learned from a database of human range scans. We demonstrate a discriminative method to directly recover the model parameters from monocular images using a conditional mixture of kernel regressors. This predicted pose and shape are used to initialize a generative model for more detailed pose and shape estimation. The resulting approach allows fully automatic pose and shape recovery from monocular and multi-camera imagery. Experimental results show that our method is capable of robustly recovering articulated pose, shape and biometric measurements (e.g.

Stability is a desirable characteristic for linear dynamical systems, but it is often ignored by algorithms that learn these systems from data. We propose a novel method for learning stable linear dynamical systems: we formulate an approximation of the problem as a convex program, start with a solution to a relaxed version of the program, and incrementally add constraints to improve stability. Rather than continuing to generate constraints until we reach a feasible solution, we test stability at each step; because the convex program is only an approximation of the desired problem, this early stopping rule can yield a higher-quality solution. We apply our algorithm to the task of learning dynamic textures from image sequences as well as to modeling biosurveillance drug-sales data. The constraint generation approach leads to noticeable improvement in the quality of simulated sequences. We compare our method to those of Lacy and Bernstein [1, 2], with positive results in terms of accuracy, quality of simulated sequences, and efficiency.

This paper compares a family of methods for characterizing neural feature selectivity with natural stimuli in the framework of the linear-nonlinear model. In this model, the neural firing rate is a nonlinear function of a small number of relevant stimulus components. The relevant stimulus dimensions can be found by maximizing one of the family of objective functions, Rényi divergences of different orders [1, 2]. We show that maximizing one of them, Rényi divergence of order 2, is equivalent to least-square fitting of the linear-nonlinear model to neural data. Next, we derive reconstruction errors in relevant dimensions found by maximizing Rényi divergences of arbitrary order in the asymptotic limit of large spike numbers. We find that the smallest errors are obtained with Rényi divergence of order 1, also known as Kullback-Leibler divergence.

Many existing approaches to collaborative filtering can neither handle very large datasets nor easily deal with users who have very few ratings. In this paper we present the Probabilistic Matrix Factorization (PMF) model which scales linearly with the number of observations and, more importantly, performs well on the large, sparse, and very imbalanced Netflix dataset. We further extend the PMF model to include an adaptive prior on the model parameters and show how the model capacity can be controlled automatically. Finally, we introduce a constrained version of the PMF model that is based on the assumption that users who have rated similar sets of movies are likely to have similar preferences. The resulting model is able to generalize considerably better for users with very few ratings. When the predictions of multiple PMF models are linearly combined with the predictions of Restricted Boltzmann Machines models, we achieve an error rate of 0.8861, that is nearly 7% better than the score of Netflix's own system.

Semantic memory refers to our knowledge of facts and relationships between concepts. A successful semantic memory depends on inferring relationships between items that are not explicitly taught. Recent mathematical modeling of episodic memory argues that episodic recall relies on retrieval of a gradually-changing representation of temporal context. We show that retrieved context enables the development of a global memory space that reflects relationships between all items that have been previously learned. When newly-learned information is integrated into this structure, it is placed in some relationship to all other items, even if that relationship has not been explicitly learned. We demonstrate this effect for global semantic structures shaped topologically as a ring, and as a two-dimensional sheet. We also examined the utility of this learning algorithm for learning a more realistic semantic space by training it on a large pool of synonym pairs. Retrieved context enabled the model to "infer" relationships between synonym pairs that had not yet been presented.

Point process encoding models provide powerful statistical methods for understanding the responses of neurons to sensory stimuli. Although these models have been successfully applied to neurons in the early sensory pathway, they have fared less well capturing the response properties of neurons in deeper brain areas, owing in part to the fact that they do not take into account multiple stages of processing. Here we introduce a new twist on the point-process modeling approach: we include unobserved as well as observed spiking neurons in a joint encoding model. The resulting model exhibits richer dynamics and more highly nonlinear response properties, making it more powerful and more flexible for fitting neural data. More importantly, it allows us to estimate connectivity patterns among neurons (both observed and unobserved), and may provide insight into how networks process sensory input. We formulate the estimation procedure using variational EM and the wake-sleep algorithm, and illustrate the model's performance using a simulated example network consisting of two coupled neurons.

Current computational models of bottom-up and top-down components of attention are predictive of eye movements across a range of stimuli and of simple, fixed visual tasks (such as visual search for a target among distractors). However, to date there exists no computational framework which can reliably mimic human gaze behavior in more complex environments and tasks, such as driving a vehicle through traffic. Here, we develop a hybrid computational/behavioral framework, combining simple models for bottom-up salience and top-down relevance, and looking for changes in the predictive power of these components at different critical event times during 4.7 hours (500,000 video frames) of observers playing car racing and flight combat video games. This approach is motivated by our observation that the predictive strengths of the salience and relevance models exhibit reliable temporal signatures during critical event windows in the task sequence--for example, when the game player directly engages an enemy plane in a flight combat game, the predictive strength of the salience model increases significantly, while that of the relevance model decreases significantly. Our new framework combines these temporal signatures to implement several event detectors. Critically, we find that an event detector based on fused behavioral and stimulus information (in the form of the model's predictive strength) is much stronger than detectors based on behavioral information alone (eye position) or image information alone (model prediction maps). This approach to event detection, based on eye tracking combined with computational models applied to the visual input, may have useful applications as a less-invasive alternative to other event detection approaches based on neural signatures derived from EEG or fMRI recordings.