We extend a previously developed Bayesian framework for perception to account for sensory adaptation. We first note that the perceptual effects ofadaptation seems inconsistent with an adjustment of the internally 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 particular, wecompare 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.

The misjudgement of tilt in images lies at the heart of entertaining visual illusionsand rigorous perceptual psychophysics. A wealth of findings has attracted many mechanistic models, but few clear computational principles. We adopt a Bayesian approach to perceptual tilt estimation, showing how a smoothness prior offers a powerful way of addressing much confusing data. In particular, we faithfully model recent results showing that confidence in estimation can be systematically affected by the same aspects of images that affect bias. Confidence is central to Bayesian modeling approaches, and is applicable in many other perceptual domains. Perceptual anomalies and illusions, such as the misjudgements of motion and tilt evident in so many psychophysical experiments, have intrigued researchers for decades.

There have been many graph-based approaches for semi-supervised classification. Oneproblem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation ofthe graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification.Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problemover the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classifier to classify new points. Tests on synthetic and real datasets show cases where there are significant improvements in performance over the existing approaches.

We consider the case in which the true distribution is contained in the learner model.

Functional Magnetic Resonance Imaging (fMRI) has enabled scientists to look into the active brain. However, interactivity between functional brain regions, is still little studied. In this paper, we contribute a novel framework for modeling the interactions between multiple active brain regions, using Dynamic Bayesian Networks (DBNs) as generative models forbrain activation patterns. This framework is applied to modeling of neuronal circuits associated with reward. The novelty of our framework froma Machine Learning perspective lies in the use of DBNs to reveal the brain connectivity and interactivity. Such interactivity models whichare derived from fMRI data are then validated through a group classification task.

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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 estimates. Wedemonstrate 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 close by briefly discussing an interesting connection to recent models of neural population coding.

We propose a new Bayesian method for spatial cluster detection, the "Bayesian spatial scan statistic," and compare this method to the standard (frequentist) scan statistic approach. We demonstrate that the Bayesian statistic has several advantages over the frequentist approach, including increased power to detect clusters and (since randomization testing is unnecessary) much faster runtime. We evaluate the Bayesian and frequentist methodson the task of prospective disease surveillance: detecting spatial clusters of disease cases resulting from emerging disease outbreaks. Wedemonstrate that our Bayesian methods are successful in rapidly detecting outbreaks while keeping number of false positives low.

Given a redundant dictionary of basis vectors (or atoms), our goal is to find maximally sparse representations of signals. Previously, we have argued that a sparse Bayesian learning (SBL) framework is particularly well-suited for this task, showing that it has far fewer local minima than other Bayesian-inspired strategies. In this paper, we provide further evidence forthis claim by proving a restricted equivalence condition, based on the distribution of the nonzero generating model weights, whereby the SBL solution will equal the maximally sparse representation. We also prove that if these nonzero weights are drawn from an approximate Jeffreys prior,then with probability approaching one, our equivalence condition issatisfied.

We present a Bayesian framework for explaining how people reason about and predict the actions of an intentional agent, based on observing itsbehavior. 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 environment. Workingin 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 quantitative predictionsthat adult observers make in a new experiment.