Related papers: Identification of a relaxation kernel using two bo…
In order to understand the long known anomalies in the composition dependence of diffusion and viscosity of binary mixtures, we introduce here two new models and carry out extensive molecular dynamic simulations. In these models, the two…
We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a…
We consider the least-square regression problem with regularization by a block 1-norm, i.e., a sum of Euclidean norms over spaces of dimensions larger than one. This problem, referred to as the group Lasso, extends the usual regularization…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
In this paper we consider an inverse problem for the time dependent linear Boltzmann equation. It concerns the identification of the coefficients via a finite number of measurements on the boundary. We prove that the total extinction…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
The notion of a two-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in non-relativistic phenomena is generalized to accommodate the constraints required of a causal formulation in…
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…
We propose a spectral-based approach to analyze how two-layer neural networks separate from linear methods in terms of approximating high-dimensional functions. We show that quantifying this separation can be reduced to estimating the…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
We consider linear scalar wave equations with a hereditary integral term of the kind used to model viscoelastic solids. The kernel in this Volterra integral is a sum of decaying exponentials (The so-called Maxwell, or Zener model) and this…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
Inspired by the article "Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel" (Z. Angew. Math. Phys. (2019) 70:42) which authors D. Zhao and HG. Sun studied the integro-differential equation with the…
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel space. A kernel typically…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary…
We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…