Gene Regulation Network Inference With Joint Sparse Gaussian Graphical Models

Sparse and Locally Constant Gaussian Graphical Models

Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). Although these datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies in the datasets. Mo...

Sparse Gaussian graphical models for speech recognition

We address the problem of learning the structure of Gaussian graphical models for use in automatic speech recognition, a means of controlling the form of the inverse covariance matrices of such systems. With particular focus on data sparsity issues, we implement a method for imposing graphical model structure on a Gaussian mixture system, using a convex optimisation technique to maximise a pena...

Edge detection in sparse Gaussian graphical models

Bayesian Learning of Sparse Gaussian Graphical Models

Sparse inverse covariance matrix modeling is an important tool for learning relationships among different variables in a Gaussian graph. Most existing algorithms are based on `1 regularization, with the regularization parameters tuned via cross-validation. In this paper, a Bayesian formulation of the problem is proposed, where the regularization parameters are inferred adaptively and cross-vali...

Approximate inference in Gaussian graphical models

The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high-dimensional systems specified through local interactions. While such models are extremely rich and...