Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are widely used to characterize the impedance and estimate parameters of electrochemical systems such as batteries. We use a generic ECM with ten parameters grouped to model ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

We consider optimal regimes for algorithm-assisted human decision-making. Such regimes are decision functions of measured pre-treatment variables and, by leveraging natural treatment values, enjoy a superoptimality property whereby they are guaranteed to o ...

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

Central aortic diastolic pressure decay time constant ( ) is according to the two-element Windkessel model equal to the product of total peripheral resistance (R) times total arterial compliance (C ). As such, it is related to arterial stiffness, which has ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

This paper presents the experimental validation of a linear recursive state estimation (SE) process for hybrid AC/DC microgrids proposed in the authors' previous work. The SE uses a unified and linear measurement model that relies on the use of synchronize ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

Selection bias may arise when data have been chosen in a way that subsequent analysis does not account for. Such bias can arise in climate event attribution studies that are performed rapidly after a devastating "trigger event'', whose occurrence correspon ...

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfil ...

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright–Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation techniques that are of s ...

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

The growing demand for online gait phase (GP) estimation, driven by advancements in exoskeletons and prostheses, has prompted numerous approaches in the literature. Some approaches explicitly use time, while others rely on state variables to estimate the G ...

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Chat with Graph Search

Spectral Estimators for High-Dimensional Matrix Inference

Stability: a search for structure

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

Random matrix methods for high-dimensional machine learning models

Optimal regimes for algorithm-assisted human decision-making

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Novel theory and potential applications of central diastolic pressure decay time constant

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Experimental Validation of a Unified and Linear State Estimation Method for Hybrid AC/DC Microgrids

An equilibrated flux a posteriori error estimator for defeaturing problems

Timing and spatial selection bias in rapid extreme event attribution

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Regularization for distributionally robust state estimation and prediction

A Shape Derivative Approach to Domain Simplification

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

ReLU Neural Network Galerkin BEM

State-Based Versus Time-Based Estimation of the Gait Phase for Hip Exoskeletons in Steady and Transient Walking