Related papers: Kernel Interpolation with Sparse Grids
We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
We present a scalable Gaussian Process (GP) method called DSoftKI that can fit and predict full derivative observations. It extends SoftKI, a method that approximates a kernel via softmax interpolation, to the setting with derivatives.…
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a $d$-dimensional tensor product space, the number of grid points is $N = \mathcal O(h^{-1} |\log h|^{d-1})$, where $h$ is a mesh parameter. The…
Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…
Graph Neural Networks (GNNs) have emerged as effective tools for learning tasks on graph-structured data. Recently, Graph-Informed (GI) layers were introduced to address regression tasks on graph nodes, extending their applicability beyond…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
Channel state information (CSI) acquisition and feedback overhead grows with the number of antennas, users, and reported subbands. This growth becomes a bottleneck for many antenna and reconfigurable intelligent surface (RIS) systems as…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…
In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…
A corpus of recent work has revealed that the learned index can improve query performance while reducing the storage overhead. It potentially offers an opportunity to address the spatial query processing challenges caused by the surge in…
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…
Sparse grids based on Lagrange polynomials have become one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, in the context e.g. of PDE-based parametric design exploration. They are…