Related papers: Diffusion Representation for Asymmetric Kernels
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Diffusion models have achieved state-of-the-art performance in generating many different kinds of data, including images, text, and videos. Despite their success, there has been limited research on how the underlying diffusion process and…
The distributional statistical framework replaces classical probability densities by distribution-kernel pairs $(T, \varphi)$, where $T$ is a tempered distribution and $\varphi$ is a rapidly decaying kernel. We develop the thesis that the…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
Wireless signals are integral to modern society, enabling both communication and increasingly, environmental sensing. While various propagation models exist, ranging from empirical methods to full-wave simulations, the phenomenon of…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
AI fairness seeks to improve the transparency and explainability of AI systems by ensuring that their outcomes genuinely reflect the best interests of users. Data augmentation, which involves generating synthetic data from existing…
Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by…
Diffusion models have emerged as state-of-the-art generative methods for image synthesis, yet their potential as general-purpose feature encoders remains underexplored. Trained for denoising and generation without labels, they can be…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
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…
We propose a novel concept of asymmetric feature maps (AFM), which allows to evaluate multiple kernels between a query and database entries without increasing the memory requirements. To demonstrate the advantages of the AFM method, we…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations in order to synthesize high-quality, high-fidelity images with improved spatial…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we…
Data fusion is an essential task in various domains, enabling the integration of multi-source information to enhance data quality and insights. One key application is in satellite remote sensing, where fusing multi-sensor observations can…