Related papers: Signal detection for inverse problems in a multidi…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…
We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of…
This paper considers an anomaly detection problem in which a detection algorithm assigns anomaly scores to multi-dimensional data points, such as cellular networks' Key Performance Indicators (KPIs). We propose an optimization framework to…
Deep neural networks have shown impressive performance for image-based disease detection. Performance is commonly evaluated through clinical validation on independent test sets to demonstrate clinically acceptable accuracy. Reporting good…
This paper investigates the inverse problem of determining a general Signorini obstacle using boundary measurements. We demonstrate that both the shape of the obstacle and the obstacle function can be uniquely determined from solution…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as the sample size grows. Despite this,…
The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…
Inverse problems are often ill-posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is…
We introduce a new statistical test based on the observed spacings of ordered data. The statistic is sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, this new test…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
This paper analyzes the robustness of recent 3D shape descriptors to SO(3) rotations, something that is fundamental to shape modeling. Specifically, we formulate the task of rotated 3D object instance detection. To do so, we consider a…
Machine learning algorithms are extensively used to make increasingly more consequential decisions about people, so achieving optimal predictive performance can no longer be the only focus. A particularly important consideration is fairness…
We propose a family of tests to assess the goodness-of-fit of a high-dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and…
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are…