Thomas P. Minka

This paper presents a new deterministic approximation technique in Bayesian networks. This method, "Expectation Propagation", unifies two previous techniques: assumed-density filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. All three algorithms try to recover an approximate distribution which is close in KL divergence to the true distribution. Loopy belief propagation, because it propagates exact belief states, is useful for a limited class of belief networks, such as those which are purely discrete. Expectation Propagation approximates the belief states by only retaining certain expectations, such as mean and variance, and iterates until these expectations are consistent throughout the network. This makes it applicable to hybrid networks with discrete and continuous nodes. Expectation Propagation also extends belief propagation in the opposite direction - it can propagate richer belief states that incorporate correlations between nodes. Experiments with Gaussian mixture models show Expectation Propagation to be convincingly better than methods with similar computational cost: Laplace's method, variational Bayes, and Monte Carlo. Expectation Propagation also provides an efficient algorithm for training Bayes point machine classifiers.

One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," unifies and generalizes two previous techniques: assumeddensity filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. The unification shows how both of these algorithms can be viewed as approximating the true posterior distribution with a simpler distribution, which is close in the sense of KL-divergence. Expectation Propagation exploits the best of both algorithms: the generality of assumed-density filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states, is useful for limited types of belief networks, such as purely discrete networks. Expectation Propagati...

This paper presents a new algorithm for the automatic recognition of object classes from images (categorization). Compact and yet discriminative appearance-based object class models are automatically learned from a set of training images. The method is simple and extremely fast, making it suitable for many applications such as semantic image retrieval, Web search, and interactive image editing. It classifies a region according to the proportions of different visual words (clusters in feature space). The specific visual words and the typical proportions in each object are learned from a segmented training set. The main contribution of this paper is twofold: i) an optimally compact visual dictionary is learned by pair-wise merging of visual words from an initially large dictionary. The final visual words are described by GMMs. ii) A novel statistical measure of discrimination is proposed which is optimized by each merge operation. High classification accuracy is demonstrated for nine object classes on photographs of real objects viewed under general lighting conditions, poses and viewpoints. The set of test images used for validation comprise: i) photographs acquired by us, ii) images from the Web and iii) images from the recently released Pascal dataset. The proposed algorithm performs well on both texture-rich objects (e.g. grass, sky, trees) and structure-rich ones (e.g. cars, bikes, planes)

The Dirichlet distribution and its compound variant, the Dirichlet-multinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximum-likelihood estimate of these distributions is not available in closed-form. This paper describes simple and efficient iterative schemes for obtaining parameter estimates in these models. In each case, a fixed-point iteration and a Newton-Raphson (or generalized Newton-Raphson) iteration is provided. 1 The Dirichlet distribution The Dirichlet distribution is a model of how proportions vary. Let p denote a random vector whose elements sum to 1, so that pk represents the proportion of item k. Under the Dirichlet model with parameter vector α, the probability density at p is p(p) ∼ D(α1,...,αK) = Γ(∑kαk) ∏ kΓ(αk) ∏ k p αk−1

This paper presents the theory, design principles, implementation and performance results of PicHunter, a prototype content-based image retrieval (CBIR) system. In addition, this document presents the rationale, design and results of psychophysical experiments that were conducted to address some key issues that arose during PicHunter's development. The PicHunter project makes four primary contributions to research on CBIR. First, PicHunter represents a simple instance of a general Bayesian framework which we describe for using relevance feedback to direct a search. With an explicit model of what users would do, given the target image they want, PicHunter uses Bayes's rule to predict the target they want, given their actions. This is done via a probability distribution over possible image targets, rather than by refining a query. Second, an entropy-minimizing display algorithm is described that attempts to maximize the information obtained from a user at each iteration of the search. Third, PicHunter makes use of hidden annotation rather than a possibly inaccurate/inconsistent annotation structure that the user must learn and make queries in. Finally, PicHunter introduces two experimental paradigms to quantitatively evaluate the performance of the system, and psychophysical experiments are presented that support the theoretical claims.