Related papers: Kernel Interpolation with Sparse Grids
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…
Modern artificial intelligence has revolutionized our ability to extract rich and versatile data representations across scientific disciplines. Yet, the statistical properties of these representations remain poorly controlled, causing…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
While most scene flow methods use either variational optimization or a strong rigid motion assumption, we show for the first time that scene flow can also be estimated by dense interpolation of sparse matches. To this end, we find sparse…
Superpixels have long been used in image simplification to enable more efficient data processing and storage. However, despite their computational potential, their irregular spatial distribution has often forced deep learning approaches to…
This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by…
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide…
In computer vision most iterative optimization algorithms, both sparse and dense, rely on a coarse and reliable dense initialization to bootstrap their optimization procedure. For example, dense optical flow algorithms profit massively in…
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…
We revisit the Gaussian process model with spherical harmonic features and study connections between the associated RKHS, its eigenstructure and deep models. Based on this, we introduce a new class of kernels which correspond to deep models…
Discrete empirical interpolation method (DEIM) estimates a function from its incomplete pointwise measurements. Unfortunately, DEIM suffers large interpolation errors when few measurements are available. Here, we introduce Sparse DEIM…
With the rise of big data sets, the popularity of kernel methods declined and neural networks took over again. The main problem with kernel methods is that the kernel matrix grows quadratically with the number of data points. Most attempts…
We develop and analyze a class of matrix-valued spherical-convolution kernels stemming from scaled zonal functions on $\mathbb{S}^2,$ the unit sphere embedded in $\mathbb{R}^3$. The construct of these kernels utilizes the Legendre…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
K-means is a popular clustering algorithm with significant applications in numerous scientific and engineering areas. One drawback of K-means is its inability to identify non-linearly separable clusters, which may lead to inaccurate…
Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and…