相关论文: Hellinger vs. Kullback-Leibler multivariable spect…

Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…

We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…

In this work we derive higher order error estimates for inverse problems distorted by non-additive noise, in terms of Bregman distances. The results are obtained by means of a novel source condition, inspired by the dual problem.…

The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem…

Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…

In many contexts Gaussian Mixtures (GM) are used to approximate probability distributions, possibly time-varying. In some applications the number of GM components exponentially increases over time, and reduction procedures are required to…

We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…

We obtain a new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters. Explicit…

This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…

We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…

Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…

We model the Knudsen layer in Kramers' problem by linearized high order hyperbolic moment system. Due to the hyperbolicity, the boundary conditions of the moment system is properly reduced from the kinetic boundary condition. For Kramers'…

The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…

We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…

This study investigates a new hybrid method for solving the combinatorial problem of optimizing fractional functions with 0-1 binary variables. The method combines density matrix minimization (DMM), tabu search (TS), and the Dinkelbach…

The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \in \mathbb{C}^{2n\times 2n}$ with a…