Related papers: A Scalable Algorithm for Gaussian Graphical Models…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…
Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…
Gaussian processes (GPs) are a highly flexible, nonparametric statistical model that are commonly used to fit nonlinear relationships or account for correlation between observations. However, the computational load of fitting a Gaussian…
Mean shift (MS) algorithms are popular methods for mode finding in pattern analysis. Each MS algorithm can be phrased as a fixed-point iteration scheme, which operates on a kernel density estimate (KDE) based on some data. The ability of an…
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…
Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval…
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. As it is known, the…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference…
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on…
The investigation of samples with a spatial resolution in the nanometer range relies on the precise and stable positioning of the sample. Due to inherent mechanical instabilities of typical sample stages in optical microscopes, it is…
We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However,…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…