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We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

We show that deterministic multimode Gaussian channels admit a symmetric-space description. Passing from the n-mode Siegel disk to a doubled version of that space lets general Gaussian dynamics act by a linear-fractional (Mobius)…

Recent work introduced deep kernel processes as an entirely kernel-based alternative to NNs (Aitchison et al. 2020). Deep kernel processes flexibly learn good top-layer representations by alternately sampling the kernel from a distribution…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

A scheme for approximating the kernel $w$ of the fractional $\alpha$-integral by a linear combination of exponentials is proposed and studied. The scheme is based on the application of a composite Gauss-Jacobi quadrature rule to an integral…

Gravitational wave detectors produce time series of the gravitational wave strain co-added with instrument noise. For evenly sampled data, such as from laser interferometers, it has been traditional to Fourier transform the data and perform…

In brain imaging, the image acquisition and processing processes themselves are likely to introduce noise to the images. It is therefore imperative to reduce the noise while preserving the geometric details of the anatomical structures for…

Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on…

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…

In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…

This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…