A Risk Minimization Principle for a Class of Parzen Estimators
Kristiaan Pelckmans, Johan A.K. Suykens and Bar t De Moor ID T16

Maximal Margin with model sign(w T X ) Y (w T Xi ) ^ M = max min i w i w2 Maximal Average Margin Classifier
n 1 X Yi (w T Xi ) ¯ M = max wn w2 i =1
X2

Uncer tainty of Prediction of (a) MAMC (b) SVM
Class prediction class 1 class 2

1

0.8

0.6

0.4

0.2

0

Closed Form Solution
n 1X T wn (X ) = Yi K (Xi , X ) n i =1

-0.2

-1.2

-1

-0.8

-0.6

-0.4

-0.2 X1

0

0.2

0.4

0.6

0.8

1

0.8

Uncer tainty of Prediction with (X ) 2  B " " B - E [Y (w T (X ))] P Y (w T (X ))  0  B Extension to Ordinal Regression
n 1X max sign(Yj -Yi )w T ((Xj )-(Xi )) s.t. wn i ,j =1
X2

0.6

0.4

0.2

0

-0.2

-1.2

-1

-0.8

-0.6

-0.4

-0.2 X1

0

0.2

0.4

0.6

0.8

w

2

1

K. Pelckmans (KULeuven - ESAT - SCD)

Average Margin Classifier

NIPS 2007

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