We describe a three-dimensional geometric hand model suitable for visual trackingapplications. The kinematic constraints implied by the model's joints have a probabilistic structure which is well described by a graphical model. Inference in this model is complicated by the hand's many degrees of freedom, as well as multimodal likelihoods caused by ambiguous image measurements. We use nonparametric belief propagation (NBP)to develop a tracking algorithm which exploits the graph's structure to control complexity, while avoiding costly discretization. While kinematic constraints naturally have a local structure, self-occlusions created by the imaging process lead to complex interpendencies incolor and edge-based likelihood functions. However, we show that local structure may be recovered by introducing binary hidden variables describingthe occlusion state of each pixel. We augment the NBP algorithm to infer these occlusion variables in a distributed fashion, and then analytically marginalize over them to produce hand position estimates whichproperly account for occlusion events. We provide simulations showing that NBP may be used to refine inaccurate model initializations, aswell as track hand motion through extended image sequences.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models.

During the last ten years there has been growing interest in the development ofBrain 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 imaginemovements 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].

In the context of binary Classification, we define disagreement as a measure of how often two independently-trained models differ in their Classification of unlabeled data.

We study the problem of hierarchical classification when labels corresponding topartial and/or multiple paths in the underlying taxonomy are allowed. We introduce a new hierarchical loss function, the H-loss, implementing thesimple intuition that additional mistakes in the subtree of a mistaken class should not be charged for. Based on a probabilistic data model introduced in earlier work, we derive the Bayes-optimal classifier for the H-loss. We then empirically compare two incremental approximations ofthe Bayes-optimal classifier with a flat SVM classifier and with classifiers obtained by using hierarchical versions of the Perceptron and SVM algorithms. The experiments show that our simplest incremental approximationof the Bayes-optimal classifier performs, after just one training epoch, nearly as well as the hierarchical SVM classifier (which performs best). For the same incremental algorithm we also derive an H-loss bound showing, when data are generated by our probabilistic data model, exponentially fast convergence to the H-loss of the hierarchical classifier based on the true model parameters.

What makes a neural microcircuit computationally powerful?

We investigate an approach for simultaneously committing to multiple activities,each modeled as a temporally extended action in a semi-Markov decision process (SMDP). For each activity we define aset of admissible solutions consisting of the redundant set of optimal policies, and those policies that ascend the optimal statevalue functionassociated with them. A plan is then generated by merging them in such a way that the solutions to the subordinate activities are realized in the set of admissible solutions satisfying the superior activities.

Statistical language models estimate the probability of a word occurring in a given context. The most common language models rely on a discrete enumeration of predictive contexts (e.g., n-grams) and consequently fail to capture and exploit statistical regularities across these contexts. In this paper, we show how to learn hierarchical, distributed representations of word contexts that maximize the predictive value of a statistical language model. The representations are initialized by unsupervised algorithms for linear and nonlinear dimensionality reduction [14], then fed as input into a hierarchical mixture of experts, where each expert is a multinomial distribution overpredicted words [12]. While the distributed representations in our model are inspired by the neural probabilistic language model of Bengio et al. [2, 3], our particular architecture enables us to work with significantly larger vocabularies and training corpora. For example, on a large-scale bigram modeling task involving a sixty thousand word vocabulary anda training corpus of three million sentences, we demonstrate consistent improvement over class-based bigram models [10, 13]. We also discuss extensions of our approach to longer multiword contexts.

We present an algorithm to perform blind, one-microphone speech separation.

A generative probabilistic model for objects in images is presented. An object consists of a constellation of features. Feature appearance and pose are modeled probabilistically. Scene images are generated by drawing aset of objects from a given database, with random clutter sprinkled on the remaining image surface.