Related papers: Kernel interpolation with continuous volume sampli…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…
Deep learning based methods have recently pushed the state-of-the-art on the problem of Single Image Super-Resolution (SISR). In this work, we revisit the more traditional interpolation-based methods, that were popular before, now with the…
The Versatile Video Coding (VVC) standard significantly improves compression efficiency over its predecessor, HEVC, but at the cost of substantially higher computational complexity, particularly in intra-frame prediction. This stage employs…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
This Note proposes a new methodology for function classification with Support Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert basis as in our previous work, we use an implicit spline interpolation that allows…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…
Determinantal point processes (DPPs) have become a significant tool for recommendation systems, feature selection, or summary extraction, harnessing the intrinsic ability of these probabilistic models to facilitate sample diversity. The…
We study approaches for compressing the empirical measure in the context of finite dimensional reproducing kernel Hilbert spaces (RKHSs). In this context, the empirical measure is contained within a natural convex set and can be…