We introduce a computationally efficient method to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size. We present numerical results that demonstrate the correctness of our estimates for the uniform random model and for a real-world network ("C.

A reactive environment is one that responds to the actions of an agent rather than evolving obliviously. In reactive environments, experts algorithms must balance exploration and exploitation of experts more carefully than in oblivious ones. In addition, a more subtle definition of a learnable value of an expert is required. A general exploration-exploitation experts method is presented along with a proper definition of value. The method is shown to asymptotically perform as well as the best available expert. Several variants are analyzed from the viewpoint of the exploration-exploitation tradeoff, including explore-then-exploit, polynomially vanishing exploration, constant-frequency exploration, and constant-size exploration phases. Complexity and performance bounds are proven.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approximation methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

We introduce a computationally efficient method to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size. We present numerical results that demonstrate the correctness of our estimates for the uniform random model and for a real-world network ("C.

We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at the dimension of the true underlying manifold. This observation suggests to explore non-local manifold learning algorithms which attempt to discover shared structure in the tangent planes at different positions. A criterion for such an algorithm is proposed and experiments estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms: it is able to generalize very far from training data (on learning handwritten character image rotations), where a local nonparametric method fails.

Planning algorithms designed for deterministic worlds, such as A* search, usually run much faster than algorithms designed for worlds with uncertain action outcomes, such as value iteration. Real-world planning problems often exhibit uncertainty, which forces us to use the slower algorithms to solve them. Many real-world planning problems exhibit sparse uncertainty: there are long sequences of deterministic actions which accomplish tasks like moving sensor platforms into place, interspersed with a small number of sensing actions which have uncertain outcomes. In this paper we describe a new planning algorithm, called MCP (short for MDP Compression Planning), which combines A* search with value iteration for solving Stochastic Shortest Path problem in MDPs with sparse stochasticity. We present experiments which show that MCP can run substantially faster than competing planners in domains with sparse uncertainty; these experiments are based on a simulation of a ground robot cooperating with a helicopter to fill in a partial map and move to a goal location.

We consider the semi-supervised learning problem, where a decision rule is to be learned from labeled and unlabeled data. In this framework, we motivate minimum entropy regularization, which enables to incorporate unlabeled data in the standard supervised learning. Our approach includes other approaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed solution benefits from unlabeled data. The method challenges mixture models when the data are sampled from the distribution class spanned by the generative model. The performances are definitely in favor of minimum entropy regularization when generative models are misspecified, and the weighting of unlabeled data provides robustness to the violation of the "cluster assumption". Finally, we also illustrate that the method can also be far superior to manifold learning in high dimension spaces.

The context in which a name appears in a caption provides powerful cues as to who is depicted in the associated image. We obtain 44,773 face images, using a face detector, from approximately half a million captioned news images and automatically link names, obtained using a named entity recognizer, with these faces. A simple clustering method can produce fair results. We improve these results significantly by combining the clustering process with a model of the probability that an individual is depicted given its context. Once the labeling procedure is over, we have an accurately labeled set of faces, an appearance model for each individual depicted, and a natural language model that can produce accurate results on captions in isolation.

During the last ten years there has been growing interest in the development of Brain Computer Interfaces (BCIs). The field has mainly been driven by the needs of completely paralyzed patients to communicate. With a few exceptions, most human BCIs are based on extracranial electroencephalography (EEG). However, reported bit rates are still low. One reason for this is the low signal-to-noise ratio of the EEG [16]. We are currently investigating if BCIs based on electrocorticography (ECoG) are a viable alternative. In this paper we present the method and examples of intracranial EEG recordings of three epilepsy patients with electrode grids placed on the motor cortex. The patients were asked to repeatedly imagine movements of two kinds, e.g., tongue or finger movements. We analyze the classifiability of the data using Support Vector Machines (SVMs) [18, 21] and Recursive Channel Elimination (RCE) [11].

We describe how we used a data set of chorale harmonisations composed by Johann Sebastian Bach to train Hidden Markov Models. Using a probabilistic framework allows us to create a harmonisation system which learns from examples, and which can compose new harmonisations. We make a quantitative comparison of our system's harmonisation performance against simpler models, and provide example harmonisations.