Spectral Algorithms for Supervised Learning

We discuss how a large class of regularization methods, collectively known as spectral regularization and originally designed for solving ill-posed inverse problems, gives rise to regularized learning algorithms. All of these algorithms are consistent kernel methods that can be easily implemented. T...

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Bibliographic Details
Published in:Neural computation 2008-07, Vol.20 (7), p.1873-1897
Main Authors: Gerfo, L. Lo, Rosasco, L., Odone, F., Vito, E. De, Verri, A.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Biological and medical sciences
Computer science
control theory
systems
Databases as Topic
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
General aspects
Learning
Learning and adaptive systems
Least-Squares Analysis
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Matrix
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Performance evaluation
Problem solving
Regression Analysis
Sciences and techniques of general use
Time Factors
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Summary:We discuss how a large class of regularization methods, collectively known as spectral regularization and originally designed for solving ill-posed inverse problems, gives rise to regularized learning algorithms. All of these algorithms are consistent kernel methods that can be easily implemented. The intuition behind their derivation is that the same principle allowing for the numerical stabilization of a matrix inversion problem is crucial to avoid overfitting. The various methods have a common derivation but different computational and theoretical properties. We describe examples of such algorithms, analyze their classification performance on several data sets and discuss their applicability to real-world problems.
ISSN:0899-7667
1530-888X
DOI:10.1162/neco.2008.05-07-517