The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly, we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification and density estimation with Gaussian processes and on an independent component analysis problem.

In this paper we introduce new algorithms for unsupervised learning based on the use of a kernel matrix. All the information required by such algorithms is contained in the eigenvectors of the matrix or of closely related matrices. We use two different but related cost functions, the Alignment and the'cut cost'. The first one is discussed in a companion paper [3], the second one is based on graph theoretic concepts. Both functions measure the level of clustering of a labeled dataset, or the correlation between data clusters and labels.

However, SVMs require to solve a quadratic optimization problem which needs resources that are at least quadratic in the number of training examples, and it is thus hopeless to try solving problems having millions of examples using classical SVMs. In order to overcome this drawback, we propose in this paper to use a mixture of several SVMs, each of them trained only on a part of the dataset. The idea of an SVM mixture is not new, although previous attempts such as Kwok's paper on Support Vector Mixtures [5] did not train the SVMs on part of the dataset but on the whole dataset and hence could not overcome the'Part of this work has been done while Ronan Collobert was at IDIAP, CP 592, rue du Simplon 4, 1920 Martigny, Switzerland.

We describe the application of kernel methods to Natural Language Processing (NLP) problems. In many NLP tasks the objects being modeled are strings, trees, graphs or other discrete structures which require some mechanism to convert them into feature vectors. We describe kernels for various natural language structures, allowing rich, high dimensional representations of these structures. We show how a kernel over trees can be applied to parsing using the voted perceptron algorithm, and we give experimental results on the ATIS corpus of parse trees.

The choice of an SVM kernel corresponds to the choice of a representation of the data in a feature space and, to improve performance, it should therefore incorporate prior knowledge such as known transformation invariances. We propose a technique which extends earlier work and aims at incorporating invariances in nonlinear kernels. We show on a digit recognition task that the proposed approach is superior to the Virtual Support Vector method, which previously had been the method of choice. 1 Introduction In some classification tasks, an a priori knowledge is known about the invariances related to the task. For instance, in image classification, we know that the label of a given image should not change after a small translation or rotation.

We propose a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hofmann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms.

We develop an intuitive geometric framework for support vector regression (SVR). By examining when ɛ-tubes exist, we show that SVR can be regarded as a classification problem in the dual space. Hard and soft ɛ-tubes are constructed by separating the convex or reduced convex hulls respectively of the training data with the response variable shifted up and down by ɛ. A novel SVR model is proposed based on choosing the max-margin plane between the two shifted datasets.

Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering.

We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected number of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite-- consider, for example, symbols being possible words appearing in English text.

We present an algorithm that induces a class of models with thin junction trees--models that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the learning process. This allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model. We illustrate the approach with applications in handwritten digit recognition and DNA splice site detection.