We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs work with both a topic covariance matrix and a document kernel matrix, learnin...

We address an approximation method for Gaussian process (GP) regression, where we approximate covariance by a block matrix such that diagonal blocks are calculated exactly while off-diagonal blocks are approximated. Partitioning input data points, we present a two-layer hierarchical model for GP regression, where prototypes of clusters in the upper layer are involved for coarse modeling by a GP...

Models of shape variations have become a central component for the automated analysis of images. An important class of shape models are point distribution models (PDMs). These models represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation...

Gaussian processes are a promising non-linear interpolation tool (Williams 1995; Williams and Rasmussen 1996), but it is not straightforward to solve classiication problems with them. In this paper the variational methods of Jaakkola and Jordan (1996) are applied to Gaussian processes to produce an eecient Bayesian binary classiier.

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the marginal likelihood of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g...

Reinforcement learning (RL) and optimal control of systems with continuous states and actions require approximation techniques in most interesting cases. In this article, we introduce Gaussian process dynamic programming (GPDP), an approximate value-function based RL algorithm. We consider both a classic optimal control problem, where problem-specific prior knowledge is available, and a classic...

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approach: Gaussian process priors are imposed over the latent functions and general...

Most existing GP regression algorithms assume a single generative model, leading to poor performance when data are nonstationary, i.e. generated from multiple switching processes. Existing methods for GP regression over non-stationary data include clustering and changepoint detection algorithms. However, these methods require significant computation, do not come with provable guarantees on corr...