Related papers: Gaussian Blur and Relative Edge Response
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…
A widely used approximation of the Gaussian curvature on a triangulated surface is the angle defect, which measures the deviation between $2\pi$ and the sum of the angles between neighboring edges emanating from a common vertex. We show…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
The boundary representation (B-Rep) models a 3D solid as its explicit boundaries: trimmed corners, edges, and faces. Recovering B-Rep representation from unstructured data is a challenging and valuable task of computer vision and graphics.…
Recent advancements in computer vision have successfully extended Open-vocabulary segmentation (OVS) to the 3D domain by leveraging 3D Gaussian Splatting (3D-GS). Despite this progress, efficiently rendering the high-dimensional features…
We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction…
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…
We give a lower bound for the Gaussian curvature of convex level sets of minimal graphs and the solutions to semilinear elliptic equations with the norm of boundary gradient and the Gaussian curvature of the boundary.
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…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
Since Bustince et al. introduced the concepts of overlap and grouping functions, these two types of aggregation functions have attracted a lot of interest in both theory and applications. In this paper, the depiction of $(O,G)$-granular…