Areas of the brain involved in various forms of memory exhibit patterns of neural activity quite unlike those in canonical computational models. We show how to use well-founded Bayesian probabilistic autoassociative recall to derive biologically reasonable neuronal dynamics in recurrently coupled models, together with appropriate values for parameters such as the membrane time constant and inhibition. We explicitly treat two cases. One arises from a standard Hebbian learning rule, and involves activity patterns that are coded by graded firing rates. The other arises from a spike timing dependent learning rule, and involves patterns coded by the phase of spike times relative to a coherent local field potential oscillation. Our model offers a new and more complete understanding of how neural dynamics may support autoassociation.

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generalization to new groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

The correction of bias in magnetic resonance images is an important problem in medical image processing. Most previous approaches have used a maximum likelihood method to increase the likelihood of the pixels in a single image by adaptively estimating a correction to the unknown image bias field. The pixel likelihoods are defined either in terms of a preexisting tissue model, or non-parametrically in terms of the image's own pixel values. In both cases, the specific location of a pixel in the image is not used to calculate the likelihoods. We suggest a new approach in which we simultaneously eliminate the bias from a set of images of the same anatomy, but from different patients. We use the statistics from the same location across different images, rather than within an image, to eliminate bias fields from all of the images simultaneously. The method builds a "multi-resolution" nonparametric tissue model conditioned on image location while eliminating the bias fields associated with the original image set.

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 errors ranging from 1.38 to 1.84Å.

Protein interactions typically arise from a physical interaction of one or more small sites on the surface of the two proteins. Identifying these sites is very important for drug and protein design. In this paper, we propose a computational method based on probabilistic relational model that attempts to address this task using high-throughput protein interaction data and a set of short sequence motifs. We learn the model using the EM algorithm, with a branch-and-bound algorithm as an approximate inference for the E-step. Our method searches for motifs whose presence in a pair of interacting proteins can explain their observed interaction. It also tries to determine which motif pairs have high affinity, and can therefore lead to an interaction. We show that our method is more accurate than others at predicting new protein-protein interactions. More importantly, by examining solved structures of protein complexes, we find that 2/3 of the predicted active motifs correspond to actual interaction sites.

Spike sorting involves clustering spike trains recorded by a microelectrode according to the source neuron. It is a complicated problem, which requires a lot of human labor, partly due to the non-stationary nature of the data. We propose an automated technique for the clustering of non-stationary Gaussian sources in a Bayesian framework. At a first search stage, data is divided into short time frames and candidate descriptions of the data as a mixture of Gaussians are computed for each frame. At a second stage transition probabilities between candidate mixtures are computed, and a globally optimal clustering is found as the MAP solution of the resulting probabilistic model. Transition probabilities are computed using local stationarity assumptions and are based on a Gaussian version of the Jensen-Shannon divergence. The method was applied to several recordings. The performance appeared almost indistinguishable from humans in a wide range of scenarios, including movement, merges, and splits of clusters.

We describe a three-dimensional geometric hand model suitable for visual tracking applications. 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 in color and edge-based likelihood functions. However, we show that local structure may be recovered by introducing binary hidden variables describing the 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 which properly account for occlusion events. We provide simulations showing that NBP may be used to refine inaccurate model initializations, as well as track hand motion through extended image sequences.

While clustering is usually an unsupervised operation, there are circumstances in which 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 clustering based 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. We fit the model parameters with EM. Experiments on a variety of data sets show that PPC can consistently improve clustering results.

Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

We present a generative model and stochastic filtering algorithm for simultaneous tracking of 3D position and orientation, nonrigid motion, object texture, and background texture using a single camera. We show that the solution to this problem is formally equivalent to stochastic filtering of conditionally Gaussian processes, a problem for which well known approaches exist [3, 8]. We propose an approach based on Monte Carlo sampling of the nonlinear component of the process (object motion) and exact filtering of the object and background textures given the sampled motion. The smoothness of image sequences in time and space is exploited by using Laplace's method to generate proposal distributions for importance sampling [7]. The resulting inference algorithm encompasses both optic flow and template-based tracking as special cases, and elucidates the conditions under which these methods are optimal. We demonstrate an application of the system to 3D nonrigid face tracking.