Related papers: Response Matrix Estimation in Unfolding Differenti…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited…
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…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
In this paper, we study the problem of uncertainty estimation and calibration for LLMs. We begin by formulating the uncertainty estimation problem, a relevant yet underexplored area in existing literature. We then propose a supervised…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…