相关论文: Prony's method under an almost sharp multivariate …

We present lower estimates for the best constant appearing in the weak $(1,1)$ maximal inequality in the space $(\R^n,\|\cdot\|_{\iy})$. We show that this constant grows to infinity faster than $(\log n)^{1-o(1)}$ when $n$ tends to…

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce…

This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…

Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…

We consider the problem of density estimation in the context of multiscale Langevin diffusion processes, where a single-scale homogenized surrogate model can be derived. In particular, our aim is to learn the density of the invariant…

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…

Pruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters.…

We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in…

The unitary NN-piNN model contains a serious theoretical flaw: unitarity is obtained at the price of having to use an effective piNN coupling constant that is smaller than the experimental one. This is but one aspect of a more general…

In this article, we consider change point inference for high dimensional linear models. For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression…

We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…