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.

Spike sorting involves Clustering spike trains recorded by a micro-electrode according to the source neuron.

In this paper we present a framework for using multi-layer perceptron (MLP)networks in nonlinear generative models trained by variational Bayesian learning. The nonlinearity is handled by linearizing it using a Gauss-Hermite quadrature at the hidden neurons. Thisyields an accurate approximation for cases of large posterior variance.The method can be used to derive nonlinear counterparts forlinear algorithms such as factor analysis, independent component/factor analysis and state-space models. This is demonstrated witha nonlinear factor analysis experiment in which even 20 sources can be estimated from a real world speech data set.

While clustering is usually an unsupervised operation, there are circumstances inwhich we believe (with varying degrees of certainty) that items A and B should be assigned to the same cluster, while items A and C should not. We would like such pairwise relations to influence cluster assignments of out-of-sample data in a manner consistent with the prior knowledge expressed in the training set. Our starting point is probabilistic clusteringbased on Gaussian mixture models (GMM) of the data distribution. We express clustering preferences in the prior distribution over assignments of data points to clusters. This prior penalizes cluster assignments according to the degree with which they violate the preferences.

This paper analyzes generalization of the Classic Rescorla-Wagner (R-W) learning algon'thm and studies their relationship to Maximum Likelihood estimation of causal parameters.

Coreference analysis, also known as record linkage or identity uncertainty, isa difficult and important problem in natural language processing, databases, citation matching and many other tasks. This paper introduces severaldiscriminative, conditional-probability models for coreference analysis,all examples of undirected graphical models. Unlike many historical approaches to coreference, the models presented here are relational--they do not assume that pairwise coreference decisions should be made independently from each other. Unlike other relational models of coreference that are generative, the conditional model here can incorporate a great variety of features of the input without having to be concerned about their dependencies--paralleling the advantages of conditional randomfields over hidden Markov models.

X-ray crystallography is currently the most common way protein structures are elucidated. One of the most time-consuming steps in the crystallographic process is interpretation of the electron density map, a task that involves finding patterns in a three-dimensional picture of a protein. This paper describes DEFT (DEFormable Template), an algorithm using pictorial structures to build a flexible protein model from the protein's amino-acid sequence. Matching this pictorial structure into the density map is a way of automating density-map interpretation. Also described are several extensions to the pictorial structure matching algorithm necessary for this automated interpretation. DEFT is tested on a set of density maps ranging from 2 to 4Å resolution, producing rootmean-squared errorsranging from 1.38 to 1.84Å.

Inference in these "exponential family harrnoniums" is

We propose a "soft greedy" learning algorithm for building small conjunctions of simple threshold functions, called rays, defined on single real-valued attributes. We also propose a PAC-Bayes risk bound which is minimized for classifiers achieving a nontrivial tradeoff between sparsity (the number of rays used) and the magnitude ofthe separating margin of each ray. Finally, we test the soft greedy algorithm on four DNA micro-array data sets.