Related papers: Sparse Inducing Points in Deep Gaussian Processes:…
Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However,…
Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
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…
We introduce Support Decomposition Variational Inference (SDVI), a new variational inference (VI) approach for probabilistic programs with stochastic support. Existing approaches to this problem rely on designing a single global variational…
The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a…
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…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data…
Blind image restoration (IR) is a common yet challenging problem in computer vision. Classical model-based methods and recent deep learning (DL)-based methods represent two different methodologies for this problem, each with their own…
While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed…
The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation…
We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections introducing the associated, statistically improved model D3-GP. We generated a data set containing interaction energies for 1,248…
Existing image restoration methods mostly leverage the posterior distribution of natural images. However, they often assume known degradation and also require supervised training, which restricts their adaptation to complex real…