213. On learning the optimal regularization parameter in inverse problems
Invited abstract in session WF-7: Regularization methods for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.
Wednesday, 16:20 - 18:00Room: M:I
Authors (first author is the speaker)
| 1. | Jonathan Chirinos Rodriguez
|
| IRIT, INP Toulouse |
Abstract
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge due to its promising results in many applications. Nevertheless, few theoretical guarantees have been provided up to date.
In this work, we provide a theoretical analysis for this problem by applying classical statistical learning techniques. In particular, we characterize the error performance of this method following an empirical risk minimization approach. We show that, provided with enough data, this approach can reach sharp rates while being essentially adaptive to the noise and smoothness of the problem. Our analysis studies a wide variety of regularization methods, including spectral regularization methods (Tikhonov regularization, Landweber iteration, the ν-method), non-linear Tikhonov regularization and general convex regularizers such as sparsity inducing
norms and Total Variation regularization. Finally, we show some numerical simulations that corroborate and illustrate the theoretical findings.
Keywords
- Optimization for learning and data analysis
- Artificial intelligence based optimization methods and appl
- Data driven optimization
Status: accepted
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