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.

We consider criteria for variational representations of non-Gaussian latent variables,and derive variational EM algorithms in general form. We establish a general equivalence among convex bounding methods, evidence basedmethods, and ensemble learning/Variational Bayes methods, which has previously been demonstrated only for particular cases.

We investigate the learning of the appearance of an object from a single image of it. Instead of using a large number of pictures of the object to recognize, we use a labeled reference database of pictures of other objects tolearn invariance to noise and variations in pose and illumination. This acquired knowledge is then used to predict if two pictures of new objects, which do not appear on the training pictures, actually display the same object. We propose a generic scheme called chopping to address this task. It relies on hundreds of random binary splits of the training set chosen to keep together the images of any given object. Those splits are extended to the complete image space with a simple learning algorithm. Given two images, the responses of the split predictors are combined with a Bayesian rule into a posterior probability of similarity.

We design a new learning algorithm for the Set Covering Machine froma PAC-Bayes perspective and propose a PAC-Bayes risk bound which is minimized for classifiers achieving a non trivial margin-sparsity tradeoff.

Theories of visual attention commonly posit that early parallel processes extract conspicuous featuressuch as color contrast and motion from the visual field. These features are then combined into a saliency map, and attention is directed to the most salient regions first. Top-down attentional control is achieved by modulating the contribution of different feature types to the saliency map. A key source of data concerning attentional control comes from behavioral studies in which the effect of recent experience is examined asindividuals repeatedly perform a perceptual discrimination task (e.g., "what shape is the odd-colored object?"). The robust finding is that repetition of features of recent trials (e.g., target color) facilitates performance. We view this facilitation as an adaptation to the statistical structure of the environment. We propose a probabilistic model of the environment that is updated after each trial. Under the assumption that attentional control operates so as to make performance more efficient for more likely environmental states, we obtain parsimonious explanations for data from four different experiments. Further, our model provides a rational explanation for why the influence of past experience on attentional control is short lived.

Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DPin which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object-centered coordinate frame, while transformations model the object positionsin a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeledstreet scenes, we show that the TDP's inclusion of spatial structure improves detection performance, flexibly exploiting partially labeled training images.

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.

There have been several attempts to circumvent some of these lacunae, for example [2, 1].