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Basket trials have emerged as a new class of efficient approaches in oncology to evaluate a new treatment in several patient subgroups simultaneously. In this paper, we extend the key ideas to disease areas outside of oncology, developing a…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable…

Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the…

Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

Sparse Gaussian Processes are a key component of high-throughput Bayesian optimisation (BO) loops -- an increasingly common setting where evaluation budgets are large and highly parallelised. By using representative subsets of the available…

Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…

In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Statistical estimates from survey samples have traditionally been obtained via design-based estimators. In many cases, these estimators tend to work well for quantities such as population totals or means, but can fall short as sample sizes…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a…

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these…

Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…

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…