6533b82ffe1ef96bd12957bc
RESEARCH PRODUCT
Learning, regularization and ill-posed inverse problems
L. RosascoAndrea CaponnettoE. VitoU. GiovanniniF. Odonesubject
Inverse problemsRegularization theoryStatistical LearningIll-Posed Inverse ProblemsSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciLearning theory; Inverse problems; Regularization TheoryLearning theoryStatistical Learning; Regularization theory; Ill-Posed Inverse ProblemsMachine learningRegularization TheorySettore FIS/03 - Fisica Della Materiadescription
Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we provide a positive answer to both questions. Indeed, considering the square loss, we translate the learning problem in the language of regularization theory and show that consistency results and optimal regularization parameter choice can be derived by the discretization of the corresponding inverse problem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-01-01 |