Related papers: On Construction of Higher Order Kernels Using Four…

We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state nuclear magnetic resonance for machine learning. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and…

We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…

Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…

Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the…

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…

In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more…

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

In the first part of the paper kernels are constructed which meromorphically extend the Macdonald-Koornwinder polynomials in their degrees. In the second part of the paper the kernels associated with rank one root systems are used to define…

This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…

We study the behavior of the shifted convolution sum involving fourth power of the Fourier coefficients of holomorphic cusp forms with a weight function to be the $k$-full kernel function for any fixed integer $k\geq2$.

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…

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…

We develop a higher order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the…

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the $d$-dimensional Euclidean space. Both the…

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks.…

Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…