In this paper, we propose a Bayesian framework, which constructs shared-state triphone HMMs based on a variational Bayesian approach, and recognizes speech based on the Bayesian prediction classification; variational Bayesian estimation and clustering for speech recognition (VBEC). An appropriate model structure with high recognition performance can be found within a VBEC framework. Unlike conventional methods, including BIC or MDL criterion based on the maximum likelihood approach, the proposed model selection is valid in principle, even when there are insufficient amounts of data, because it does not use an asymptotic assumption. In isolated word recognition experiments, we show the advantage of VBEC over conventional methods, especially when dealing with small amounts of data.

We consider the general problem of utilizing both labeled and unlabeled data to improve classification accuracy. Under t he assumption that the data lie on a submanifold in a high dimensional space, we develop an algorithmic framework to classify a partially labeled data set in a principled manner. The central idea of our approach is that classification functions are naturally defined only on t he submanifold in question rather than the total ambient space. Using the Laplace Beltrami operator one produces a basis for a Hilbert space of square integrable functions on the submanifold. To recover such a basis, only unlabeled examples are required. Once a basis is obtained, training can be performed using the labeled data set. Our algorithm models the manifold using the adjacency graph for the data and approximates the Laplace Beltrami operator by the graph Laplacian. Practical applications to image and text classification are considered.

A distance-based conditional model on the ranking poset is presented for use in classification and ranking. The model is an extension of the Mallows model, and generalizes the classifier combination methods used by several ensemble learning algorithms, including error correcting output codes, discrete AdaBoost, logistic regression and cranking. The algebraic structure of the ranking poset leads to a simple Bayesian interpretation of the conditional model and its special cases. In addition to a unifying view, the framework suggests a probabilistic interpretation for error correcting output codes and an extension beyond the binary coding scheme.

In this paper we present a new algorithm suitable for matching discrete objects such as strings and trees in linear time, thus obviating dynarrtic programming with quadratic time complexity. Furthermore, prediction cost in many cases can be reduced to linear cost in the length of the sequence to be classified, regardless of the number of support vectors. This improvement on the currently available algorithms makes string kernels a viable alternative for the practitioner.

We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.

A new family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. Based on the heat equation on the Riemannian manifold defined by the Fisher information metric, information diffusion kernels generalize the Gaussian kernel of Euclidean space, and provide a natural way of combining generative statistical modeling with nonparametric discriminative learning. As a special case, the kernels give a new approach to applying kernel-based learning algorithms to discrete data. Bounds on covering numbers for the new kernels are proved using spectral theory in differential geometry, and experimental results are presented for text classification.

We introduce a general family of kernels based on weighted transducers or rational relations, rational kernels, that can be used for analysis of variable-length sequences or more generally weighted automata, in applications such as computational biology or speech recognition. We show that rational kernels can be computed efficiently using a general algorithm of composition of weighted transducers and a general single-source shortest-distance algorithm. We also describe several general families of positive definite symmetric rational kernels. These general kernels can be combined with Support Vector Machines to form efficient and powerful techniques for spoken-dialog classification: highly complex kernels become easy to design and implement and lead to substantial improvements in the classification accuracy. We also show that the string kernels considered in applications to computational biology are all specific instances of rational kernels.

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured by the identity of the clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without any need to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classical results, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cells is functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.

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.

In this paper we show how the generation of documents can be thought of as a k-stage Markov process, which leads to a Fisher kernel from which the n-gram and string kernels can be reconstructed. The Fisher kernel view gives a more flexible insight into the string kernel and suggests how it can be parametrised in a way that reflects the statistics of the training corpus. Furthermore, the probabilistic modelling approach suggests extending the Markov process to consider subsequences of varying length, rather than the standard fixed-length approach used in the string kernel. We give a procedure for determining which subsequences are informative features and hence generate a Finite State Machine model, which can again be used to obtain a Fisher kernel. By adjusting the parametrisation we can also influence the weighting received by the features. In this way we are able to obtain a logarithmic weighting in a Fisher kernel. Finally, experiments are reported comparing the different kernels using the standard Bag of Words kernel as a baseline.