learning the kernel matrix with semi-definite programmingover the convex cone of positive...

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IMA, March 12, 2003 Gert Lanckriet ([email protected] ) Nello Cristianini, Peter Bartlett, Laurent El Ghaoui, Michael Jordan U.C. Berkeley Learning the Kernel Matrix with Semi-Definite Programming

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Page 1: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

IMA, March 12, 2003

Gert Lanckriet ([email protected])Nello Cristianini, Peter Bartlett, Laurent El Ghaoui, Michael Jordan

U.C. Berkeley

Learning the Kernel Matrix with Semi-Definite

Programming

Page 2: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 3: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Machine learning

Kernel-based machine learning

Page 4: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 5: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 6: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

training set (labelled)

test set (unlabelled)

Page 7: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 8: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 9: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 10: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 11: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 12: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 13: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 14: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 15: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 16: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 17: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 18: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 19: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 20: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Optimization

Learning the kernel matrix !

Learning

Page 21: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

training set (labelled)

test set (unlabelled)

Learning the kernel matrix !

Page 22: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 23: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 24: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 25: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 26: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 27: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 28: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 29: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 30: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 31: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 32: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 33: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

Page 34: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

QPLP

QCQP

SDPSOCP

Page 35: Learning the Kernel Matrix with Semi-Definite Programmingover the convex cone of positive semi-definite matrices or convex subsets of this cone) empirical results on standard benchmark

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