T34 Multi-Task Learning via Conic Programming
Tsuyoshi Kato, Hisashi Kashima, Masashi Sugiyama, Kiyoshi Asai
Univ of Tokyo IBM TRL Tokyo Tech Univ of Tokyo, AIST CBRC

Learn with a task network Related tasks are connected in the task network Trained via a Second Order Cone Programming
True Classification Boundaries
1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1 1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1 1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1 1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1 1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

Independently Learned SVMs
1 0.5 0 -0.5 -1 -1 -0.5 0
1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1

1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

Multi-Task Learning without Task Network
1 0.5 0 -0.5 -1 -1 -0.5 0
1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1

Multi-Task Learning with Task Network
1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0
1 0.5 0 -0.5

1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1

1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0 1 0.5 0 -0.5
0.5 1

1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0 1 0.5 0 -0.5 0.5 1 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

1 0.5 0 -0.5 -1 -1 -0.5 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 0.5 1

-1 -1 -0.5 0

-1 -1 -0.5 0