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Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated…

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…

Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…

iffusion-based generative models increasingly rely on inference-time guidance, adding a drift term or reweighting mixture of experts, to improve sample quality on task-specific objectives. However, most existing techniques require repeated…

In many areas of science, complex phenomena are modeled by stochastic parametric simulators, often featuring high-dimensional parameter spaces and intractable likelihoods. In this context, performing Bayesian inference can be challenging.…

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…