Related papers: Kernel Interpolation of High Dimensional Scattered…
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…
Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…
The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume {\it all the data are already in one place}, and…
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…
Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
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.…
Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems…
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous convergence. To this end, we find the class of kernels and the structure of…
This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…