Related papers: Bayes Blocks: An Implementation of the Variational…
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…
Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…
This paper reviews background and examples of Bayesian predictive synthesis (BPS), and develops details in a subset of BPS mixture models. BPS expands on standard Bayesian model uncertainty analysis for model mixing to provide a broader…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if…