Related papers: Convergence of Multilevel Stationary Gaussian Conv…

We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for…

Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…

The interpolation of high-dimensional potential energy surfaces (PESs) is commonly done with physically-inspired deep-neural network models. In this work, we illustrate that Gaussian Processes (GPs) are also capable of interpolating…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Deep features have been proven powerful in building accurate dense semantic correspondences in various previous works. However, the multi-scale and pyramidal hierarchy of convolutional neural networks has not been well studied to learn…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…

Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian,…

This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…

Kernel interpolation, especially in the context of Gaussian process emulation, is a widely used technique in surrogate modelling, where the goal is to cheaply approximate an input-output map using a limited number of function evaluations.…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…

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…

Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…

In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…

This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a system of partial differential equations (PDEs) can…

Recently, enthusiastic studies have devoted to texture synthesis using deep neural networks, because these networks excel at handling complex patterns in images. In these models, second-order statistics, such as Gram matrix, are used to…

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…