Related papers: A modified discrepancy principle to attain optimal…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
Points in the unit cube with low discrepancy can be constructed using algebra or, more recently, by direct computational optimization of a criterion. The usual $L_\infty$ star discrepancy is a poor criterion for this because it is…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
Consider a target moving at a constant velocity on a unit-circumference circle, starting at an arbitrary location. To acquire the target, any region of the circle can be probed to obtain a noisy measurement of the target's presence, where…
A range counting problem is specified by a set $P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an integer weight $x_p$ associated to each point $p \in P$, and a range space ${\cal R} \subseteq 2^{P}$. Given a query range $R \in {\cal…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression…
As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it…
We consider the sound ranging, or source localization, problem --- find the unknown source-point from known moments when the spherical wave of linearly, with time, increasing radius reaches known sensor-points --- in some non-proper metric…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…