We describe a new algorithmic framework for learning multiclass categorization problems. In this framework a multiclass predictor is composed of a pair of embeddings that map both instances and labels into a common space. In this space each instance is assigned the label it is nearest to. We outline and analyze an algorithm, termed Bunching, for learning the pair of embeddings from labeled data. A key construction in the analysis of the algorithm is the notion of probabilistic output codes, a generalization of error correcting output codes (ECOC). Furthermore, the method of multiclass categorization using ECOC is shown to be an instance of Bunching. We demonstrate the advantage of Bunching over ECOC by comparing their performance on numerous categorization problems.

We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized - which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to lI-SVM when the number of classes k 2. Both approaches are optimal in size of 21 where I is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.

We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SS

This algorithm-the "single-class minimax probability machine (MPM)"- is built on a distribution-free methodology that minimizes the worst-case probability of a data point falling outside of a convex set, given only the mean and covariance matrix of the distribution and making no further distributional assumptions. We present a robust approach to estimating the mean and covariance matrix within the general two-class MPM setting, and show how this approach specializes to the single-class problem. We provide empirical results comparing the single-class MPM to the single-class SVM and a two-class SVM method. 1 Introduction Novelty detection is an important unsupervised learning problem in which test data are to be judged as having been generated from the same or a different process as that which generated the training data.

Missing data is common in real-world datasets and is a problem for many estimation techniques. We have developed a variational Bayesian method to perform Independent Component Analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Modeling the distributions of the independent sources with mixture of Gaussians allows sources to be estimated with different kurtosis and skewness. The variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems. This allows direct probability estimation of missing values in the high dimensional space and avoids dimension reduction preprocessing which is not feasible with missing data.

We show the existence of critical points as lines for the likelihood function of mixture-type models. They are given by embedding of a critical point for models with less components. A sufficient condition that the critical line gives local maxima or saddle points is also derived. Based on this fact, a component-split method is proposed for a mixture of Gaussian components, and its effectiveness is verified through experiments.

The problem of extracting the relevant aspects of data, in face of multiple conflicting structures, is inherent to modeling of complex data. Extracting structure in one random variable that is relevant for another variable has been principally addressed recently via the information bottleneck method [15]. However, such auxiliary variables often contain more information than is actually required due to structures that are irrelevant for the task. In many other cases it is in fact easier to specify what is irrelevant than what is, for the task at hand. Identifying the relevant structures, however, can thus be considerably improved by also minimizing the information about another, irrelevant, variable. In this paper we give a general formulation of this problem and derive its formal, as well as algorithmic, solution. Its operation is demonstrated in a synthetic example and in two real world problems in the context of text categorization and face images. While the original information bottleneck problem is related to rate distortion theory, with the distortion measure replaced by the relevant information, extracting relevant features while removing irrelevant ones is related to rate distortion with side information.

Low rank approximation techniques are widespread in pattern recognition research -- they include Latent Semantic Analysis (LSA), Probabilistic LSA, Principal Components Analysus (PCA), the Generative Aspect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally "unsupervised," which allows them to model data in the absence of labels or categories. With many practical problems, however, some prior knowledge is available in the form of context. In this paper, I describe a principled approach to incorporating such information, and demonstrate its application to PCA-based approximations of several data sets.

In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models. For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference for Bayesian Networks') which allows a wide variety of probabilistic models to be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations. We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

We formulate the regression problem as one of maximizing the minimum probability, symbolized by Ω, that future predicted outputs of the regression model will be within some ε bound of the true regression function. Our formulation is unique in that we obtain a direct estimate of this lower probability bound Ω. The proposed framework, minimax probability machine regression (MPMR), is based on the recently described minimax probability machine classification algorithm [Lanckriet et al.] and uses Mercer Kernels to obtain nonlinear regression models. MPMR is tested on both toy and real world data, verifying the accuracy of the Ω bound, and the efficacy of the regression models.