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.

Rosasco L., Caponnetto A., De Vito E., De Giovannini U., Odone F. (2005). Learning, regularization and ill-posed inverse problems. In M.I.L. Jordan, S. Solla (a cura di), Advances in Neural Information Processing Systems. Neural information processing systems foundation.

Learning, regularization and ill-posed inverse problems

De Giovannini U.;Odone F.
2005-01-01

Abstract

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.
2005
9780262561457
Rosasco L., Caponnetto A., De Vito E., De Giovannini U., Odone F. (2005). Learning, regularization and ill-posed inverse problems. In M.I.L. Jordan, S. Solla (a cura di), Advances in Neural Information Processing Systems. Neural information processing systems foundation.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/543102
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