IMA, March 12, 2003 Gert Lanckriet ( [email protected] )

IMA, March 12, 2003

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

JordanU.C. Berkeley

Learning the Kernel Matrix with Semi-

Definite Programming

Learning the Kernel Matrix with SDP

Introduction: the idea (1)

Machine learning

Kernel-based machine learning

Introduction: the idea (2)

Introduction: the idea (3)

training set (labelled)

test set (unlabelled)

Introduction: the idea (4)

Introduction: the idea (5)

Learning the Kernel Matrix with SDP

Semi-Definite Programming (SDP)

SDP - hard margin SVM classifiers (1)

SDP - hard margin SVM classifiers (2)

SDP - hard margin SVM classifiers (3)

SDP - hard margin SVM classifiers (4)

SDP - hard margin SVM classifiers (5)

SDP - hard margin SVM classifiers (6)

Reminder: Schur complement lemma

SDP - hard margin SVM classifiers (7)

SDP !

SDP - hard margin SVM classifiers (8)

Learning the Kernel Matrix with SDP

Optimization

Learning the kernel matrix !

Learning

LKM - hard margin SVM classifiers (1)

training set (labelled)

test set (unlabelled)

Learning the kernel matrix !

LKM - hard margin SVM classifiers (2)

?

LKM - hard margin SVM classifiers (3)

LKM - hard margin SVM classifiers (4)

LKM - hard margin SVM classifiers (4)

LKM - hard margin SVM classifiers (4)

LKM - hard margin SVM classifiers (5)

LKM - hard margin SVM classifiers (6)

LKM - hard margin SVM classifiers (7)

Learning Kernel Matrix with SDP !

Learning the Kernel Matrix with SDP

Empirical results hard margin SVMs

Learning the Kernel Matrix with SDP

Conclusions and future directions

Conclusions and future directions

See also