Related papers: Finer-Grained Hardness of Kernel Density Estimatio…
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among…
We study the time complexity of the discrete $k$-center problem and related (exact) geometric set cover problems when $k$ or the size of the cover is small. We obtain a plethora of new results: - We give the first subquadratic algorithm for…
The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…
Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…
Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows…
We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number $c$ and the weak closure number $\gamma$ [Fox et…
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size…
Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires $\mathcal{O}(N)$ operations on a dataset…
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…
Knowledge graph (KG) embedding methods which map entities and relations to unique embeddings in the KG have shown promising results on many reasoning tasks. However, the same embedding dimension for both dense entities and sparse entities…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
The efficiency of Bayesian optimization (BO) relies heavily on the choice of the Gaussian process (GP) kernel, which plays a central role in balancing exploration and exploitation under limited evaluation budgets. Traditional BO methods…