相关论文: Random Parametrization Double Tensors Integrals an…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

In this paper, we provide three applications for $f$-divergences: (i) we introduce Sanov's upper bound on the tail probability of the sum of independent random variables based on super-modular $f$-divergence and show that our generalized…

We introduce tensor generalized bilateral inverses (TGBIs) under the Einstein tensor product as an extension of generalized bilateral inverses (GBIs) in the matrix environment. Moreover, the TBGI class includes so far considered composite…

A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

In a recent paper by the author (Chen in JHEP 02:115, 2020), the reduction of Feynman integrals in the parametric representation was considered. Tensor integrals were directly parametrized by using a generator method. The resulting…

We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For…

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…

We construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated…

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms…

Finite mixture models are widely used for unsupervised learning, but maximum likelihood estimation via EM suffers from degeneracy as components collapse. We introduce transcendental regularization, a penalized likelihood framework with…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

A new way to design parameter estimators with enhanced performance is proposed in the paper. The procedure consists of two stages, first, the generation of new regression forms via the application of a dynamic operator to the original…

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT)…

Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to…

In this paper, we compute the H- and Z-eigenvalues of even order symmetric tensors by using the adaptive cubic regularization algorithm.

In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique…

Two-dimensional (2D) resonant gratings enable dual angular tunability by controlling the plane of incidence (POI) under linear polarization. If the POI is set to be perpendicular to the electric field vector (s-polarization or transverse…