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Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
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…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
This paper studies the convergence rate of a message-passing distributed algorithm for solving a large-scale linear system. This problem is generalised from the celebrated Gaussian Belief Propagation (BP) problem for statistical learning…
We propose a novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model. This new approach can be equally applied to rejection-based ABC and to popular regression…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
Graph-based diffusion models have shown promising results in terms of generating high-quality solutions to NP-complete (NPC) combinatorial optimization (CO) problems. However, those models are often inefficient in inference, due to the…
We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…