Related papers: Positive Definite Kernels and Random Sequences Con…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…
We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on with the observables of a…
$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
We introduce a class of non-commutative Heisenberg like infinite dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the…
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…
We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…
This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…
In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…
A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
The seminal theorem of I.J. Schoenberg characterizes positive definite (p.d.) kernels on the unit sphere $S^{n-1}$ invariant under the automorphisms of the sphere. We obtain two generalizations of this theorem for p.d. kernels on fiber…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…