相关论文: Minimax optimal estimator in the stochastic invers…
In this paper, we study the minimax rates and provide an implementable convex algorithm for Poisson inverse problems under weak sparsity and physical constraints. In particular we assume the model $y_i \sim \mbox{Poisson}(Ta_i^{\top}f^*)$…
We study properties of an attractive-repulsive energy functional based on power-kernels, which can be used for halftoning of images. In the first part of this work, using a variational framework for probability measures, we examine…
Previous methods decompose the blind super-resolution (SR) problem into two sequential steps: \textit{i}) estimating the blur kernel from given low-resolution (LR) image and \textit{ii}) restoring the SR image based on the estimated kernel.…
We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific…
We introduce a computer-assisted proof for the required number of electrodes for uniqueness and global reconstruction for the inverse Robin transmission problem, where the corrosion function on the boundary of an interior object is to be…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…
A possibility of a few MeV electron beam diagnostics (Lorentz factor ~ 10) using polarization characteristics of the optical transition radiation (OTR) have been considered. Determinaton of the electron beam divergence have been performed…
We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle:…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared…
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…
In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…
Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…
The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…
Convex relaxations of the optimal finger selection algorithm are proposed for a minimum mean square error (MMSE) Rake receiver in an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an…
Installation of capacitors in distribution networks is one of the most used procedure to compensate reactive power generated by loads and, consequently, to reduce technical losses. So, the problem consists in identifying the optimal…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…