We describe a nonparametric Bayesian approach to generalizing from few labeled examples, guided by a larger set of unlabeled objects and the assumption of a latent tree-structure to the domain. The tree (or a distribution over trees) may be inferred using the unlabeled data. A prior over concepts generated by a mutation process on the inferred tree(s) allows efficient computation of the optimal Bayesian classification function from the labeled examples. We test our approach on eight real-world datasets.

We consider situations where training data is abundant and computing resources are comparatively scarce. We argue that suitably designed online learning algorithms asymptotically outperform any batch learning algorithm. Both theoretical and experimental evidences are presented.

The problem of approximating the product of several Gaussian mixture distributions arises in a number of contexts, including the nonparametric belief propagation (NBP) inference algorithm and the training of product of experts models. This paper develops two multiscale algorithms for sampling from a product of Gaussian mixtures, and compares their performance to existing methods. The first is a multiscale variant of previously proposed Monte Carlo techniques, with comparable theoretical guarantees but improved empirical convergence rates. The second makes use of approximate kernel density evaluation methods to construct a fast approximate sampler, which is guaranteed to sample points to within a tunable parameter ɛ of their true probability. We compare both multiscale samplers on a set of computational examples motivated by NBP, demonstrating significant improvements over existing methods.

We introduce an information theoretic method for nonparametric, nonlinear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method determines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data.

Standard approaches to object detection focus on local patches of the image, and try to classify them as background or not. We propose to use the scene context (image as a whole) as an extra source of (global) information, to help resolve local ambiguities. We present a conditional random field for jointly solving the tasks of object detection and scene classification.

Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information.

Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) - a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold.

Despite the popularity of connectionist models in cognitive science, their performance can often be difficult to evaluate. Inspired by the geometric approach to statistical model selection, we introduce a conceptually similar method to examine the global behavior of a connectionist model, by counting the number and types of response patterns it can simulate. The Markov Chain Monte Carlo-based algorithm that we constructed Þnds these patterns efficiently. We demonstrate the approach using two localist network models of speech perception.

We propose a novel method of dimensionality reduction for supervised learning. Given a regression or classification problem in which we wish to predict a variable Y from an explanatory vector X, we treat the problem of dimensionality reduction as that of finding a low-dimensional "effective subspace" of X which retains the statistical relationship between X and Y. We show that this problem can be formulated in terms of conditional independence. To turn this formulation into an optimization problem, we characterize the notion of conditional independence using covariance operators on reproducing kernel Hilbert spaces; this allows us to derive a contrast function for estimation of the effective subspace. Unlike many conventional methods, the proposed method requires neither assumptions on the marginal distribution of X, nor a parametric model of the conditional distribution of Y.

A recent area of significant progress in speaker recognition is the use of high level features--idiolect, phonetic relations, prosody, discourse structure, etc. A speaker not only has a distinctive acoustic sound but uses language in a characteristic manner. Large corpora of speech data available in recent years allow experimentation with long term statistics of phone patterns, word patterns, etc. of an individual. We propose the use of support vector machines and term frequency analysis of phone sequences to model a given speaker. To this end, we explore techniques for text categorization applied to the problem. We derive a new kernel based upon a linearization of likelihood ratio scoring. We introduce a new phone-based SVM speaker recognition approach that halves the error rate of conventional phone-based approaches.