Related papers: Going With the Flow: Normalizing Flows for Gaussia…
Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with…
This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
We propose parameterizing the population distribution of the gravitational wave population modeling framework (Hierarchical Bayesian Analysis) with a normalizing flow. We first demonstrate the merit of this method on illustrative…
The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Mat\'{e}rn kernel, that is commonly used…
Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…
Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…
Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…
Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…
Gaussian Process Regression (GPR) is an important type of supervised machine learning model with inherent uncertainty measure in its predictions. We propose a new framework, nuGPR, to address the well-known challenge of high computation…
Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…