When trying to recover 3D structure from a set of images, the most difficult problem is establishing the correspondence between the measurements. Most existing approaches assume that features can be tracked across frames, whereas methods that exploit rigidity constraints to facilitate matching do so only under restricted camera motion. In this paper we propose a Bayesian approach that avoids the brittleness associated with singling out one "best" correspondence, and instead consider the distribution over all possible correspondences. We treat both a fully Bayesian approach that yields a posterior distribution, and a MAP approach that makes use of EM to maximize this posterior. We show how Markov chain Monte Carlo methods can be used to implement these techniques in practice, and present experimental results on real data.

We establish a principled framework for adaptive transform coding. Transformcoders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design.Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model we derive a transform coding algorithm, which is a constrained version of the generalized Lloyd algorithm for vector quantizer design. A byproduct of our derivation is the introduction ofa new transform basis, which unlike other transforms (PCA, DCT, etc.) is explicitly optimized for coding. Image compression experiments show adaptive transform coders designed with our algorithm improvecompressed image signal-to-noise ratio up to 3 dB compared to global transform coding and 0.5 to 2 dB compared to other adaptive transform coders. 1 Introduction Compression algorithms for image and video signals often use transform coding as a low-complexity alternative to vector quantization (VQ).

We develop an approach for a sparse representation for Gaussian Process (GP) models in order to overcome the limitations of GPs caused by large data sets. The method is based on a combination of a Bayesian online algorithm togetherwith a sequential construction of a relevant subsample of the data which fully specifies the prediction of the model. Experimental resultson toy examples and large real-world datasets indicate the efficiency of the approach.

We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD).A mathematical programming formulation based on the observation thatKFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm.

The concept of averaging over classifiers is fundamental to the Bayesian analysis of learning. Based on this viewpoint, it has recently beendemonstrated for linear classifiers that the centre of mass of version space (the set of all classifiers consistent with the training set) - also known as the Bayes point - exhibits excellent generalisationabilities. In this paper we present a method based on the simple perceptron learning algorithm which allows to overcome this algorithmic drawback. The method is algorithmically simpleand is easily extended to the multi-class case. We present experimental results on the MNIST data set of handwritten digitswhich show that Bayes point machines (BPMs) are competitive with the current world champion, the support vector machine.

HUlna Lodhi John Shawe-Taylor N ello Cristianini Chris Watkins Department of Computer Science Royal Holloway, University of London Egham, Surrey TW20 OEX, UK {huma, john, nello, chrisw}Cdcs.rhbnc.ac.uk Abstract We introduce a novel kernel for comparing two text documents. The kernel is an inner product in the feature space consisting of all subsequences of length k. A subsequence is any ordered sequence ofk characters occurring in the text though not necessarily contiguously. The subsequences are weighted by an exponentially decaying factor of their full length in the text, hence emphasising those occurrences which are close to contiguous. A direct computation ofthis feature vector would involve a prohibitive amount of computation even for modest values of k, since the dimension of the feature space grows exponentially with k. The paper describes how despite this fact the inner product can be efficiently evaluated by a dynamic programming technique.

High dimensional data modeling is difficult mainly because the so-called "curse of dimensionality". We propose a technique called "Gaussianization" forhigh dimensional density estimation, which alleviates the curse of dimensionality by exploiting the independence structures in the data. Gaussianization is motivated from recent developments in the statistics literature: projection pursuit, independent component analysis and Gaussian mixturemodels with semi-tied covariances. We propose an iterative Gaussianizationprocedure which converges weakly: at each iteration, thedata is first transformed to the least dependent coordinates and then each coordinate is marginally Gaussianized by univariate techniques.

The product of experts learning procedure [1] can discover a set of stochastic binary features that constitute a nonlinear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, it is helpful to learn a hierarchy of separate models for each digit class. Each model in the hierarchy has one layer of hidden units and the nth level model is trained on data that consists of the activities of the hidden units in the already trained (n - l)th level model. After training, eachlevel produces a separate, unnormalized log probabilty score. With a three-level hierarchy for each of the 10 digit classes, a test image produces 30 scores which can be used as inputs to a supervised, logistic classificationnetwork that is trained on separate data. On the MNIST database, our system is comparable with current state-of-the-art discriminative methods,demonstrating that the product of experts learning procedure can produce effective generative models of high-dimensional data. 1 Learning products of stochastic binary experts Hinton [1] describes a learning algorithm for probabilistic generative models that are composed ofa number of experts. Each expert specifies a probability distribution over the visible variables and the experts are combined by multiplying these distributions together and renormalizing.

When trying to recover 3D structure from a set of images, the most difficult problem is establishing the correspondence between the measurements. Most existing approaches assume that features can be tracked across frames, whereas methods that exploit rigidity constraints to facilitate matching do so only under restricted camera motion.In this paper we propose a Bayesian approach that avoids the brittleness associated with singling out one "best" correspondence, andinstead consider the distribution over all possible correspondences. We treat both a fully Bayesian approach that yields a posterior distribution, and a MAP approach that makes use of EM to maximize this posterior. We show how Markov chain Monte Carlo methods can be used to implement these techniques in practice, and present experimental results on real data.

These methods are compared on their performance on a visual speech recognition task. While the representations developed are specific to visual speech recognition, the methods themselvesare general purpose and applicable to other tasks. Our focus is on low-level data-driven methods based on the statistical properties of relatively untouched images, as opposed to approaches that work with contours or highly processed versions of the image. Padgett [8] and Bartlett [1] systematically studied statistical methods for developing representations on expression recognition tasks. They found that local wavelet-like representations consistently outperformed global representations, like eigenfaces. In this paper we also compare local versus global representations.