Publications related to A Bayesian numerical homogenization method for elliptic multiscale inverse problems

Related publications (25)

ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference

Whereas the ability of deep networks to produce useful predictions on many kinds of data has been amply demonstrated, estimating the reliability of these predictions remains challenging. Sampling approaches such as MC-Dropout and Deep Ensembles have emerge ...

2024

Stochastic pairwise preference convergence in Bayesian agents

Max-Olivier Hongler

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

2024

An Unbiased Method of Measuring the Ratio of Two Data Sets

Jean-Paul Richard Kneib, Huanyuan Shan

In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio R between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, and the decay rate of gravitational ...

IOP Publishing Ltd2023

Robust Outlier Rejection for 3D Registration with Variational Bayes

Mathieu Salzmann, Jiancheng Yang, Zheng Dang, Zhen Wei

Learning-based outlier (mismatched correspondence) rejection for robust 3D registration generally formulates the outlier removal as an inlier/outlier classification problem. The core for this to be successful is to learn the discriminative inlier/outlier f ...

Ieee Computer Soc2023

Higher Order Asymptotics: Applications to Satellite Conjunction and Boundary Problems

Soumaya Elkantassi

Higher-order asymptotics provide accurate approximations for use in parametric statistical modelling. In this thesis, we investigate using higher-order approximations in two-specific settings, with a particular emphasis on the tangent exponential model. ...

EPFL2023

Filtered data and eigenfunction estimators for statistical inference of multiscale and interacting diffusion processes

Andrea Zanoni

We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...

EPFL2022

Statistical limits of high-dimensional inference problems

Clément Dominique Luneau

This thesis focuses on two kinds of statistical inference problems in signal processing and data science. The first problem is the estimation of a structured informative tensor from the observation of a noisy tensor in which it is buried. The structure com ...

EPFL2021

Drift Estimation of Multiscale Diffusions Based on Filtered Data

Assyr Abdulle, Andrea Zanoni, Giacomo Garegnani

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coeffic ...

2023

Discrete-Choice Mining of Social Processes

Victor Kristof

Poor decisions and selfish behaviors give rise to seemingly intractable global problems, such as the lack of transparency in democratic processes, the spread of conspiracy theories, and the rise in greenhouse gas emissions. However, people are more predict ...

EPFL2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

Fast Bayesian estimation of spatial count data models

Rico Krüger

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Mont ...

2021

Quantifying the information impact of future searches for exoplanetary biosignatures

Claudio Grimaldi

One of the major goals for astronomy in the next decades is the remote search for biosignatures (i.e., the spectroscopic evidence of biological activity) in exoplanets. Here we adopt a Bayesian statistical framework to discuss the implications of such futu ...

National Academy of Sciences2020

Bayesian regression explains how human participants handle parameter uncertainty

Michael Herzog, Jean-Pascal Théodor Pfister, Maya Anna Jastrzebowska, Mattew Pachai

Author summary How do humans make prediction when the critical factor that influences the quality of the prediction is hidden? Here, we address this question by conducting a simple psychophysical experiment in which participants had to extrapolate a parabo ...

2020

Penalization and Bayesian numerical methods for multiscale inverse problems

Andrea Di Blasio

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...

EPFL2019

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

Assyr Abdulle, Andrea Di Blasio

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

SIAM PUBLICATIONS2019

Exploration and Inference in Spatial Extremes Using Empirical Basis Functions

Emeric Rolland Georges Thibaud

Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to explore and model ...

SPRINGER2019

Statistical Aspects of Wasserstein Distances

Victor Panaretos, Yoav Zemel

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover th ...

ANNUAL REVIEWS2019

Uncertainty reduction in biochemical kinetic models: Enforcing desired model properties

Vassily Hatzimanikatis, Ljubisa Miskovic, Michaël Roger Germain Moret

A persistent obstacle for constructing kinetic models of metabolism is uncertainty in the kinetic properties of enzymes. Currently, available methods for building kinetic models can cope indirectly with uncertainties by integrating data from different biol ...

2019

Contributions to Likelihood-Based Modelling of Extreme Values

Léo Raymond-Belzile

xtreme value analysis is concerned with the modelling of extreme events such as floods and heatwaves, which can have large impacts. Statistical modelling can be useful to better assess risks even if, due to scarcity of measurements, there is inherently ver ...

EPFL2019

Accurate and efficient interpretation of load-test data for asset-management

Sai Ganesh Sarvotham Pai

Increasing demand for new infrastructure and ageing of existing infrastructure has made management of infrastructure a key challenge of this century. Replacement of all ageing civil infrastructure is economically and environmentally unsustainable. Civil in ...

EPFL2019