There is growing evidence from psychophysical and neurophysiological studies that the brain utilizes Bayesian principles for inference and de- cision making. An important open question is how Bayesian inference for arbitrary graphical models can be implemented in networks of spik- ing neurons. In this paper, we show that recurrent networks of noisy integrate-and-fire neurons can perform approximate Bayesian inference for dynamic and hierarchical graphical models. The membrane potential dynamics of neurons is used to implement belief propagation in the log domain. The spiking probability of a neuron is shown to approximate the posterior probability of the preferred state encoded by the neuron, given past inputs.

We propose a novel a framework for deriving approximations for in- tractable probabilistic models. This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1, 2, 3] and expectation propagation (EP) [4, 5]. The free energy is constructed from two approximating distributions which encode different aspects of the intractable model such a single node con- straints and couplings and are by construction consistent on a chosen set of moments. We test the framework on a difficult benchmark problem with binary variables on fully connected graphs and 2D grid graphs. We find good performance using sets of moments which either specify fac- torized nodes or a spanning tree on the nodes (structured approximation).

We present a discriminative part-based approach for the recognition of object classes from unsegmented cluttered scenes. Objects are modeled as flexible constellations of parts conditioned on local observations found by an interest operator. For each object class the probability of a given assignment of parts to local features is modeled by a Conditional Ran- dom Field (CRF). We propose an extension of the CRF framework that incorporates hidden variables and combines class conditional CRFs into a unified framework for part-based object recognition. The parameters of the CRF are estimated in a maximum likelihood framework and recogni- tion proceeds by finding the most likely class under our model.

In this paper we propose a probabilistic model for online document clus- tering. We use non-parametric Dirichlet process prior to model the grow- ing number of clusters, and use a prior of general English language model as the base distribution to handle the generation of novel clusters. Furthermore, cluster uncertainty is modeled with a Bayesian Dirichlet- multinomial distribution. We use empirical Bayes method to estimate hyperparameters based on a historical dataset. Our probabilistic model is applied to the novelty detection task in Topic Detection and Tracking (TDT) and compared with existing approaches in the literature.

We discuss a method for obtaining a subject's a priori beliefs from his/her behavior in a psychophysics context, under the assumption that the behavior is (nearly) optimal from a Bayesian perspective. The method is nonparametric in the sense that we do not assume that the prior belongs to any fixed class of distributions (e.g., Gaussian). Despite this increased generality, the method is relatively simple to implement, being based in the simplest case on a linear programming algorithm, and more generally on a straightforward maximum likelihood or maximum a posteriori formulation, which turns out to be a convex optimization problem (with no non-global local maxima) in many important cases. In addition, we develop methods for analyzing the uncertainty of these esti- mates. We demonstrate the accuracy of the method in a simple simulated coin-flipping setting; in particular, the method is able to precisely track the evolution of the subject's posterior distribution as more and more data are observed.

We present a Bayesian framework for explaining how people reason about and predict the actions of an intentional agent, based on observ- ing its behavior. Action-understanding is cast as a problem of inverting a probabilistic generative model, which assumes that agents tend to act rationally in order to achieve their goals given the constraints of their en- vironment. Working in a simple sprite-world domain, we show how this model can be used to infer the goal of an agent and predict how the agent will act in novel situations or when environmental constraints change. The model provides a qualitative account of several kinds of inferences that preverbal infants have been shown to perform, and also fits quantita- tive predictions that adult observers make in a new experiment.

Humans are extremely adept at learning new skills by imitating the actions of others. A progression of imitative abilities has been observed in children, ranging from imitation of simple body movements to goalbased imitation based on inferring intent. In this paper, we show that the problem of goal-based imitation can be formulated as one of inferring goals and selecting actions using a learned probabilistic graphical model of the environment. We first describe algorithms for planning actions to achieve a goal state using probabilistic inference. We then describe how planning can be used to bootstrap the learning of goal-dependent policies by utilizing feedback from the environment.

We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between observers both empirically, and using two kinds of models: a Bayesian approach for change detection and a family of cognitively plausible fast and frugal models. Some individuals detect too many changes and hence perform sub-optimally due to excess variability. Other individuals do not detect enough changes, and perform sub-optimally because they fail to notice short-term temporal trends.

We extend a previously developed Bayesian framework for perception to account for sensory adaptation. We first note that the perceptual ef- fects of adaptation seems inconsistent with an adjustment of the inter- nally represented prior distribution. Instead, we postulate that adaptation increases the signal-to-noise ratio of the measurements by adapting the operational range of the measurement stage to the input range. We show that this changes the likelihood function in such a way that the Bayesian estimator model can account for reported perceptual behavior. In particu- lar, we compare the model's predictions to human motion discrimination data and demonstrate that the model accounts for the commonly observed perceptual adaptation effects of repulsion and enhanced discriminability.

There have been many graph-based approaches for semi-supervised clas- sification. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, trans- formation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semi- supervised classification. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an in- ference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification.