Related papers: Forward Operator Estimation in Generative Models w…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent…

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…

Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases. Standard nonlinear regression in constitutive modeling requires considerable high-quality data and an explicit form of…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…

To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

Many machine learning methods have been recently developed to circumvent the high computational cost of the gradient-based topology optimization. These methods typically require extensive and costly datasets for training, have a difficult…

In light of the recent advancements in machine learning, we propose a novel approach to neutron source distribution estimation through the utilisation of probabilistic generative models. The estimation is based on a Monte Carlo particle…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions…

We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with…

Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single…

Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the…