We present a mathematical analysis of a class of Gibbs sampler algorithms for nonparametric mixtures, which use Dirichlet process priors and have updating steps which are partially discrete and partially continuous. We prove that such Gibbs samplers are uniformly ergodic, and we give a quantitative bound on their convergence rate. In a special case we can give a much sharper quantitative bound;...

Computers trained to reduce the noise in micrographs can now tackle fresh data by themselves.

In many graph-based semi-supervised learning algorithms, edge weights are assumed to be fixed and determined by the data points’ (often symmetric) relationships in input space, without considering directionality. However, relationships may be more informative in one direction (e.g. from labelled to unlabelled) than in the reverse direction, and some relationships (e.g. strong weights between op...

We study matrix sketching methods for regularized variants of linear regression, low rank approximation, and canonical correlation analysis. Our main focus is on sketching techniques which preserve the objective function value for regularized problems, which is an area that has remained largely unexplored. We study regularization both in a fairly broad setting, and in the specific context of th...