Classification with partially labeled data requires using a large number of unlabeled examples (or an estimated marginal P (x)), to further constrain the conditional P (y x) beyond a few available labeled examples. We formulate a regularization approach to linking the marginal and the conditional in a general way. The regularization penalty measures the information that is implied about the labels over covering regions. No parametric assumptions are required and the approach remains tractable even for continuous marginal densities P (x). We develop algorithms for solving the regularization problem for finite covers, establish a limiting differential equation, and exemplify the behavior of the new regularization approach in simple cases.

We propose a model that can learn parts-based representations of highdimensional data. Our key assumption is that the dimensions of the data can be separated into several disjoint subsets, or factors, which take on values independently of each other. We assume each factor has a small number of discrete states, and model it using a vector quantizer. The selected states of each factor represent the multiple causes of the input. Given a set of training examples, our model learns the association of data dimensions with factors, as well as the states of each VQ. Inference and learning are carried out efficiently via variational algorithms.

We present a class of algorithms for learning the structure of graphical models from data. The algorithms are based on a measure known as the kernel generalized variance (KGV), which essentially allows us to treat all variables on an equal footing as Gaussians in a feature space obtained from Mercer kernels. Thus we are able to learn hybrid graphs involving discrete and continuous variables of arbitrary type. We explore the computational properties of our approach, showing how to use the kernel trick to compute the relevant statistics in linear time. We illustrate our framework with experiments involving discrete and continuous data.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean field approach to the intractable classification model that is expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.

AdaBoost [3] minimizes an upper error bound which is an exponential function of the margin on the training set [14]. However, the ultimate goal in applications of pattern classification is always minimum error rate. On the other hand, AdaBoost needs an effective procedure for learning weak classifiers, which by itself is difficult especially for high dimensional data. In this paper, we present a novel procedure, called FloatBoost, for learning a better boosted classifier. FloatBoost uses a backtrack mechanism after each iteration of AdaBoost to remove weak classifiers which cause higher error rates. The resulting float-boosted classifier consists of fewer weak classifiers yet achieves lower error rates than AdaBoost in both training and test. We also propose a statistical model for learning weak classifiers, based on a stagewise approximation of the posterior using an overcomplete set of scalar features. Experimental comparisons of FloatBoost and AdaBoost are provided through a difficult classification problem, face detection, where the goal is to learn from training examples a highly nonlinear classifier to differentiate between face and nonface patterns in a high dimensional space. The results clearly demonstrate the promises made by FloatBoost over AdaBoost.

We propose a framework for classifier design based on discriminative densities for representation of the differences of the class-conditional distributions in a way that is optimal for classification. The densities are selected from a parametrized set by constrained maximization of some objective function which measures the average (bounded) difference, i.e. the contrast between discriminative densities. We show that maximization of the contrast is equivalent to minimization of an approximation of the Bayes risk.

Well-known applications include part-of-speech (POS) tagging, named entity classification, information extraction, text segmentation and phoneme classification in text and speech processing [7] as well as problems like protein homology detection, secondary structure prediction or gene classification in computational biology [3]. Up to now, the predominant formalism for modeling and predicting label sequences has been based on Hidden Markov Models (HMMs) and variations thereof. Yet, despite its success, generative probabilistic models - of which HMMs are a special case - have two major shortcomings, which this paper is not the first one to point out. First, generative probabilistic models are typically trained using maximum likelihood estimation (MLE) for a joint sampling model of observation and label sequences. As has been emphasized frequently, MLE based on the joint probability model is inherently non-discriminative and thus may lead to suboptimal prediction accuracy. Secondly, efficient inference and learning in this setting often requires to make questionable conditional independence assumptions.

In this paper we introduce methodology to determine the bifurcation structure of optima for a class of similar cost functions from Rate Distortion Theory, Deterministic Annealing, Information Distortion and the Information Bottleneck Method. We also introduce a numerical algorithm which uses the explicit form of the bifurcating branches to find optima at a bifurcation point.

We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sample data into locally linear low-dimensional patches, merge these patches into a single lowdimensional coordinate system, and compute forward and reverse mappings between the sample and coordinate spaces. The objective functions are convex and their solutions are given in closed form.

Gaussian process regression allows a simple analytical treatment of exact Bayesian inference and has been found to provide good performance, yet scales badly with the number of training data. In this paper we compare several approaches towards scaling Gaussian processes regression to large data sets: the subset of representers method, the reduced rank approximation, online Gaussian processes, and the Bayesian committee machine. Furthermore we provide theoretical insight into some of our experimental results. We found that subset of representers methods can give good and particularly fast predictions for data sets with high and medium noise levels. On complex low noise data sets, the Bayesian committee machine achieves significantly better accuracy, yet at a higher computational cost.