Related papers: Incomplete Gamma Kernels: Generalizing Locally Opt…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…
We design Local LMO - a new projection-free gradient-type method for constrained optimization. The key algorithmic idea is to replace the global linear minimization oracle over the constraint set used by Frank-Wolfe (FW) with a local linear…
Conformal prediction is a framework that provides valid uncertainty quantification for general models with exchangeable data. However, in the online learning and time-series settings, exchangeability is not satisfied. Existing online…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
This paper presents a LiDAR odometry estimation framework called Generalized LOAM. Our proposed method is generalized in that it can seamlessly fuse various local geometric shapes around points to improve the position estimation accuracy…
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in various applications. For example, these kernels have been…
Local learning, which trains a network through layer-wise local targets and losses, has been studied as an alternative to backpropagation (BP) in neural computation. However, its algorithms often become more complex or require additional…
A local median decomposition is used to prove that a weighted local mean of a function is controlled by a weighted local mean of its local sharp maximal function. Together with (a local version of) the estimate $M^{\sharp}_{0,s}(Tf)(x) \le…
We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-$L_p$ spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
Advancements in the generation quality of various Generative Models (GMs) has made it necessary to not only perform binary manipulation detection but also localize the modified pixels in an image. However, prior works termed as passive for…
Recent GPU generations deliver significantly higher FLOPs using lower-precision arithmetic, such as FP8. While successfully applied to large language models (LLMs), its adoption in large recommendation models (LRMs) has been limited. This…
Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…