Related papers: Convergence in variation for the multidimensional …
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
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…
In this paper we study Tikhonov regularization for the stable solution of an ill-posed non-linear operator equation. The operator we consider, which is related to an active contour model for image segmentation, is continuous, compact, but…
Determinantal point processes (DPPs) have become a significant tool for recommendation systems, feature selection, or summary extraction, harnessing the intrinsic ability of these probabilistic models to facilitate sample diversity. The…
In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is…
$L^p$ to $L^p_{\beta}$ boundedness theorems are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
This article discusses the convergence properties of the Max Product and Max Min variants of Durrmeyer type exponential sampling series. We first establish pointwise and uniform convergence of both operators in the space of log uniformly…
In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several…
This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions…
Starting from the approach to the Laplacian with respect to coupling measures and undirected weighted graphs, we provide a setting for a general point of view for a Kirchhoff type divergence and a Laplace operators built on the trivial…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…
This paper studies the expected $L_p$-discrepancy ($2 \leq p < \infty$) for stratified sampling schemes under importance sampling. We introduce a parametric family of equivolume partitions $\Omega_{\theta,\sim}$ and leverage recent exact…
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained…
The convergence theory for the gradient sampling algorithm is extended to directionally Lipschitz functions. Although directionally Lipschitz functions are not necessarily locally Lipschitz, they are almost everywhere differentiable and…
We present a machine-learning method for the nonparametric extraction of generalized parton distributions (GPDs) from Compton form factors (CFFs) constrained by experimental data. The method addresses the longstanding inverse problem posed…
The main objective of this work is to introduce the generalized convolution with trigonometric weighted $\gamma=\sin y$ involving the Fourier cosine-sine and Kontorovich-Lebedev transforms, and to study its fundamental results. We establish…