Related papers: A global structure-preserving kernel method for th…
Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…
This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field.…
In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising…
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel…
We develop a variational framework to understand the properties of the functions learned by neural networks fit to data. We propose and study a family of continuous-domain linear inverse problems with total variation-like regularization in…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
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…
This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex…
Establishing a theoretical analysis that explains why deep learning can outperform shallow learning such as kernel methods is one of the biggest issues in the deep learning literature. Towards answering this question, we evaluate excess…
This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…
We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations,…
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…
Many of the tools available for robot learning were designed for Euclidean data. However, many applications in robotics involve manifold-valued data. A common example is orientation; this can be represented as a 3-by-3 rotation matrix or a…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
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…