Related papers: Gaussian process deconvolution
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…
Multitask Gaussian processes (MTGP) are the Gaussian process (GP) framework's solution for multioutput regression problems in which the $T$ elements of the regressors cannot be considered conditionally independent given the observations.…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…
We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…
We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging,…
Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
Layer decomposition to separate an input image into base and detail layers has been steadily used for image restoration. Existing residual networks based on an additive model require residual layers with a small output range for fast…
This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…
In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process.…
Gaussian Processes (GPs) are a versatile and popular method in Bayesian Machine Learning. A common modification are Sparse Variational Gaussian Processes (SVGPs) which are well suited to deal with large datasets. While GPs allow to…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
Obstacle-aware trajectory navigation is crucial for many systems. For example, in real-world navigation tasks, an agent must avoid obstacles, such as furniture in a room, while planning a trajectory. Gaussian Process (GP) regression, in its…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…