HIERARCHICAL P E N A L I Z AT I O N
M. Szafranski, Y. Grandvalet and P.Morizet-Mahoudeaux
Poster ID T42

P ROB LEM · Input variables organized in a hierarchy (WordNet, Gene Ontology) · Discard irrelevant variables from the model
0 1,1 1,2 1 2,1 x
1

A P P R OAC H · Minimize a penalized training error · Subject to sparsness constraints
· among groups (1b) · within groups (1c)

1,3 2 2,2 2,4 2,3 x
2

3 2,5 2,8 2,62,7
4

x

3

x

x

5

x

6

x

7

x

8

J1 (d1 = 1 )

J2 (d2 = 3 )

J3 (d3 = 4 )

    min   ,          s . t.              

L ( ) +  kK

kK j

=1 Jk



2 j

1,k 2,j

(1a)

dk 1,k = 1, 2,j = 1,

=1 jd =1

1,k  0 2,j  0

(1b) (1c)

· Convex and sparse