Greedy approximation algorithms have been frequently used to obtain sparse solutions to learning problems. In this paper, we present a general greedy algorithm for solving a class of convex optimization problems. We derive a bound on the rate of approximation for this algorithm, and show that our algorithm includes a number of earlier studies as special cases.

We present a new approach to the supervised learning of lateral interactions for the competitive layer model (CLM) dynamic feature binding architecture. The method is based on consistency conditions, which were recently shown to characterize the attractor states of this linear threshold recurrent network. For a given set of training examples the learning problem is formulated as a convex quadratic optimization problem in the lateral interaction weights. An efficient dimension reduction of the learning problem can be achieved by using a linear superposition of basis interactions. We show the successful application of the method to a medical image segmentation problem of fluorescence microscope cell images.

The information bottleneck method is an unsupervised model independent data organization technique. Given a joint distribution peA, B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. In a recent paper, we introduced a general principled framework for multivariate extensions of the information bottleneck method that allows us to consider multiple systems of data partitions that are interrelated. In this paper, we present a new family of simple agglomerative algorithms to construct such systems of interrelated clusters. We analyze the behavior of these algorithms and apply them to several real-life datasets.

Many domains are naturally organized in an abstraction hierarchy or taxonomy, where the instances in "nearby" classes in the taxonomy are similar. In this paper, we provide a general probabilistic framework for clustering data into a set of classes organized as a taxonomy, where each class is associated with a probabilistic model from which the data was generated. The clustering algorithm simultaneously optimizes three things: the assignment of data instances to clusters, the models associated with the clusters, and the structure of the abstraction hierarchy. A unique feature of our approach is that it utilizes global optimization algorithms for both of the last two steps, reducing the sensitivity to noise and the propensity to local maxima that are characteristic of algorithms such as hierarchical agglomerative clustering that only take local steps. We provide a theoretical analysis for our algorithm, showing that it converges to a local maximum of the joint likelihood of model and data.

One way to attempt to achieve this is via a generative approach in which one makes distributional assumptions about the class-conditional densities and thereby estimates and controls the relevant probabilities. The need to make distributional assumptions, however, casts doubt on the generality and validity of such an approach, and in discriminative solutions to classification problems it is common to attempt to dispense with class-conditional densities entirely. Rather than avoiding any reference to class-conditional densities, it might be useful to attempt to control misclassification probabilities in a worst-case setting; that is, under all possible choices of class-conditional densities. Such a minimax approach could be viewed as providing an alternative justification for discriminative approaches. In this paper we show how such a minimax programme can be carried out in the setting of binary classification. Our approach involves exploiting the following powerful theorem due to Isii [6], as extended in recent work by Bertsimas - http://robotics.eecs.berkeley.edur

We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification, regression, and novelty detection. The inclusion of the -trick allows us to give a robust parameterization.

In many scientific and engineering applications, detecting and understanding differences between two groups of examples can be reduced to a classical problem of training a classifier for labeling new examples while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data captured by the discriminative model. However, such analysis is crucial if we want to understand and visualize the detected differences. We propose an approach to interpretation of the statistical model in the original feature space that allows us to argue about the model in terms of the relevant changes to the input vectors. For each point in the input space, we define a discriminative direction to be the direction that moves the point towards the other class while introducing as little irrelevant change as possible with respect to the classifier function. We derive the discriminative direction for kernel-based classifiers, demonstrate the technique on several examples and briefly discuss its use in the statistical shape analysis, an application that originally motivated this work.

Factor analysis and principal components analysis can be used to model linear relationships between observed variables and linearly map high-dimensional data to a lower-dimensional hidden space. In factor analysis, the observations are modeled as a linear combination of normally distributed hidden variables. We describe a nonlinear generalization of factor analysis, called "product analysis", that models the observed variables as a linear combination of products of normally distributed hidden variables. Just as factor analysis can be viewed as unsupervised linear regression on unobserved, normally distributed hidden variables, product analysis can be viewed as unsupervised linear regression on products of unobserved, normally distributed hidden variables. The mapping between the data and the hidden space is nonlinear, so we use an approximate variational technique for inference and learning.

In this paper we introduce a new sparseness inducing prior which does not involve any (hyper)parameters that need to be adjusted or estimated. Although other applications are possible, we focus here on supervised learning problems: regression and classification. Experiments with several publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms support vector machines and performs competitively with the best alternative techniques, both in terms of error rates and sparseness, although it involves no tuning or adjusting of sparsenesscontrolling hyper-parameters.

The nearest neighbor technique is a simple and appealing method to address classification problems. It relies on the assumption of locally constant class conditional probabilities. This assumption becomes invalid in high dimensions with a finite number of examples due to the curse of dimensionality. We propose a technique that computes a locally flexible metric by means of Support Vector Machines (SVMs). The maximum margin boundary found by the SVM is used to determine the most discriminant direction over the query's neighborhood. Such direction provides a local weighting scheme for input features.