The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

This paper presents lottery scheduling, a novel randomized resource allocation mechanism. Lottery scheduling provides efficient, responsive control over the relative execution rates of computations. Such control is beyond the capabilities of conventional schedulers, and is desirable in systems that service requests of varying importance, such as databases, media-based applications, and networks. Lottery scheduling also supports modular resource management by enabling concurrent modules to insulate their resource allocation policies from one another. A currency abstraction is introduced to flexibly name, share, and protect resource rights. We also show that lottery scheduling can be generalized to manage many diverse resources, such as I/O bandwidth, memory, and access to locks. We have implemented a prototype lottery scheduler for the Mach 3.0 microkernel, and found that it provides flexible and responsive control over the relative execution rates of a wide range of applications. The overhead imposed by our unoptimized prototype is comparable to that of the standard Mach timesharing policy.

Building animation tools for fluid-like motions is an important and challenging problem with many applications in computer graphics. The use of physics-based models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluid-like behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow real-time interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluid-like flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluid-like animations interactively in two- and three-dimensions.

The availability of massive amounts of DNA sequence information has begun to revolutionize the practice of biology. As a result, current large-scale sequencing output, while impressive, is not adequate to keep pace with growing demand and, in particular, is far short of what will be required to obtain the 3-billion-base human genome sequence by the target date of 2005. To reach this goal, improved automation will be essential, and it is particularly important that human involvement in sequence data processing be significantly reduced or eliminated. Progress in this respect will require both improved accuracy of the data processing software and reliable accuracy measures to reduce the need for human involvement in error correction and make human review more efficient. Here, we describe one step toward that goal: a base-calling program for automated sequencer traces, phred, with improved accuracy. phred appears to be the first base-calling program to achieve a lower error rate than the ABI software, averaging 40%–50 % fewer errors in the data sets examined independent of position in read, machine running conditions, or sequencing chemistry.

Often, the training procedure for statistical machine translation models is based on maximum likelihood or related criteria. A general problem of this approach is that there is only a loose relation to the final translation quality on unseen text. In this paper, we analyze various training criteria which directly optimize translation quality.

The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.

Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibration-free representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, M-estimators and random sampling, and the paper develops the theory required to apply them to non-linear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practitioner to guess at their value. The second goal is therefore to compare and judge the methods. Comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth. A variety of error measures are examined. The experiments allow a statistically satisfying and quasi-optimal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined. The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers.

We present new techniques for creating photorealistic textured 3D facial models from photographs of a human subject, and for creating smooth transitions between different facial expressions by morphing between these different models. Starting from several uncalibrated views of a human subject, we employ a user-assisted technique to recover the camera poses corresponding to the views as well as the 3D coordinates of a sparse set of chosen locations on the subject's face. A scattered data interpolation technique is then used to deform a generic face mesh to fit the particular geometry of the subject's face. Having recovered the camera poses and the facial geometry, we extract from the input images one or more texture maps for the model. This process is repeated for several facial expressions of a particular subject. To generate transitions between these facial expressions we use 3D shape morphing between the corresponding face models, while at the same time blending the corresponding tex...