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We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…

By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…

Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…

This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex…

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…

Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…

Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

This study addresses the computational challenges of forecasting volatility in high-dimensional commodity markets. Building on the Network log-ARCH framework, we introduce a novel class of network topologies from GARCH-informed correlation…

Optimizing the discriminator in Generative Adversarial Networks (GANs) to completion in the inner training loop is computationally prohibitive, and on finite datasets would result in overfitting. To address this, a common update strategy is…

Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

Particle Flow Filters estimate the ``a posteriori" probability density function (PDF) by moving an ensemble of particles according to the likelihood. Particles are propagated under the system dynamics until a measurement becomes available…

The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…

The quest for biologically plausible deep learning is driven, not just by the desire to explain experimentally-observed properties of biological neural networks, but also by the hope of discovering more efficient methods for training…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two…

The post-Newtonian formalism plays an integral role in the models used to extract information from gravitational wave data, but models that incorporate this formalism are inherently approximations. Disagreement between an approximate model…

This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the…