This paper introduces kernels on attributed pointsets, which are sets of vectors embedded in an euclidean space. The embedding gives the notion of neighborhood, which is used to define positive semidefinite kernels on pointsets. Two novel kernels on neighborhoods are proposed, one evaluating the attribute similarity and the other evaluating shape similarity. Shape similarity function is motivated from spectral graph matching techniques. The kernels are tested on three real life applications: face recognition, photo album tagging, and shot annotation in video sequences, with encouraging results.

We describe an efficient learning procedure for multilayer generative models that combine the best aspects of Markov random fields and deep, directed belief nets. The generative models can be learned one layer at a time and when learning is complete they have a very fast inference procedure for computing a good approximation to the posterior distribution in all of the hidden layers. Each hidden layer has its own MRF whose energy function is modulated by the top-down directed connections from the layer above. To generate from the model, each layer in turn must settle to equilibrium given its top-down input. We show that this type of model is good at capturing the statistics of patches of natural images.

Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allows a practical solution to the inference problem, {while still retaining a good degree of accuracy.} We illustrate our approach on two biologically motivated systems.

We develop and analyze an algorithm for nonparametric estimation of divergence functionals and the density ratio of two probability distributions. Our method is based on a variational characterization of f-divergences, which turns the estimation intoa penalized convex risk minimization problem. We present a derivation of our kernel-based estimation algorithm and an analysis of convergence rates for the estimator. Our simulation results demonstrate the convergence behavior of the method, which compares favorably with existing methods in the literature.

We investigate the problem of learning a widely-used latent-variable model - the Latent Dirichlet Allocation (LDA) or "topic" model - using distributed computation, whereeach of

A non--linear dynamic system is called contracting if initial conditions are forgotten exponentially fast, so that all trajectories converge to a single trajectory.

We propose a Gaussian process (GP) framework for robust inference in which a GP prior on the mixing weights of a two-component noise model augments the standard process over latent function values. This approach is a generalization of the mixture likelihood used in traditional robust GP regression, and a specialization of the GP mixture models suggested by Tresp (2000) and Rasmussen and Ghahramani (2002). The value of this restriction is in its tractable expectation propagation updates, which allow for faster inference and model selection, and better convergence than the standard mixture. An additional benefit over the latter method lies in our ability to incorporate knowledge of the noise domain to influence predictions, and to recover with the predictive distribution information about the outlier distribution via the gating process. The model has asymptotic complexity equal to that of conventional robust methods, but yields more confident predictions on benchmark problems than classical heavy-tailed models and exhibits improved stability for data with clustered corruptions, for which they fail altogether. We show further how our approach can be used without adjustment for more smoothly heteroscedastic data, and suggest how it could be extended to more general noise models. We also address similarities with the work of Goldberg et al. (1998), and the more recent contributions of Tresp, and Rasmussen and Ghahramani.

We construct a biologically motivated stochastic differential model of the neural and hemodynamic activity underlying the observed Blood Oxygen Level Dependent (BOLD) signal in Functional Magnetic Resonance Imaging (fMRI). The model poses a difficult parameter estimation problem, both theoretically due to the nonlinearity and divergence of the differential system, and computationally due to its time and space complexity. We adapt a particle filter and smoother to the task, and discuss some of the practical approaches used to tackle the difficulties, including use of sparse matrices and parallelisation. Results demonstrate the tractability of the approach in its application to an effective connectivity study.

We present an efficient generalization of the sparse pseudo-input Gaussian process (SPGP)model developed by Snelson and Ghahramani [1], applying it to binary classification problems.

The problem of obtaining the maximum a posteriori estimate of a general discrete randomfield (i.e. a random field defined using a finite and discrete set of labels) is known to be