About
What statisticians, numericians, engineers or econometricians mean by "inverse problem" often differs.
For a statistician, an inverse problem is an estimation problem of a function which is not directly observed. The data are finite in number and contain errors, whose variance decreases with the number of observations, as they do in classical inference problems, while the unknown typically is infinite dimensional, as it is in nonparametric regression.
For numericians, the noise is more an error induced by the fact that the real data are not directly observed. But the asymptotics differ, as the regularity conditions imposed for the solution.
Finally, in econometrics the structural approach combines data observation and economic model. The parameter of interest is defined as a solution of a functional equation depending on the data distribution. Hence the operator in the underlying inverse problem is in general unknown.
Many questions arise naturally in all the different fields, which are of great both applied and theoretical interest: identifiability, consistency and optimality in various forms, iterative methods. There have been great advances in the study of inverse problems within these three communities and we think that it is time for a workshop where the different point of views could be confronted, leading to exchanges of methodologies and several improvements. For instance non linear inverse problems have been studied in numerical analysis while statistical literature on this topics is scarce. Unknown inverse operators are common in econometrics but the problem is not well studied in statistics. On the other hand, adaptive estimation and optimal rates of convergence are common in statistics but not in the other fields.
Videos
Lectures

Iterative Regularization Scheme and Early Stopping in Learning from Examples
Feb 25, 2007
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3557 views

Statistical Analysis of Non Injective Inverse Problems
Feb 25, 2007
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3908 views

Nonparametric Transformation to White Noise
Feb 25, 2007
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3268 views

Inverse Problems with Error in the Operator
Feb 25, 2007
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3162 views

Methods and Convergence Results for Non Linear Inverse Problems
Feb 25, 2007
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3432 views

Inverse Problems in Biology
Feb 25, 2007
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32758 views

Testing Parametric Models in Statistical Inverse Problems
Feb 25, 2007
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3446 views

A Statistical View of Some Regularization Methods for Ill-posed Problem
Feb 25, 2007
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3633 views

Multiresolution Methods for Inverse Problems
Feb 25, 2007
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3265 views

Estimation of the Solution of a Differential Equation: an Inverse Problem
Feb 25, 2007
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28118 views

An Introduction to Instrumental Variables
Feb 25, 2007
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4791 views

Learning Theory and Inverse Problems
Feb 25, 2007
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3712 views

Regularization: Quadratic Versus Sparsity-enforcing and Deterministic Versus Sto...
Feb 25, 2007
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5354 views

Bayesian Methods for Inverse Problems
Feb 25, 2007
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6070 views

Principal Component and the Long Run
Feb 25, 2007
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5395 views

Nonparametric Additive Models for Panels of Time Series
Feb 25, 2007
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3777 views

Asymptotic Normality of a Nonparametric Instrumental Variables Estimator
Feb 25, 2007
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3888 views

Risk Hull Method for Inverse Problems
Feb 25, 2007
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3046 views

Convergence Rate in the Prokhorov Metric for Illposed Problems
Feb 25, 2007
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2984 views

Nonparametric Estimation of the Regression Function in an Errors-in-variables
Feb 25, 2007
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3183 views

Introduction
Feb 25, 2007
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3008 views