2. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
2
3. Features = elements to evaluate positions in
games
◦ e.g. Numbers and arrangements of pieces in Shogi
Difficulty in creating features
◦ Require expert knowledge for the game
◦ Simple linear combinations are insufficient
e.g. XOR
3
4. Use kernels for evaluation features in games
◦ Simple inputs
Tree structure
◦ Expect to work as non-linear features
Implicit classification in high level feature space
4
5. Classification of moves in mahjong using SVM
with kernels
◦ “Evaluation functions > search” in mahjong
Kernel method is effective
◦ Tree kernels for tree structures of mahjong hands
Similarity representation by kernel functions
◦ Use expert game records
Learn “expert moves > other moves” with SVM
5
6. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
6
7. Machine learning using simple features
◦ TD-Gammon [Tesauro, 1992]
Research about mahjong
◦ Learning from expert records [Kitagawa, 2007]
7
10. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
11
11. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
12
12. 2-class linear classifier
13
bxwxg
)(
0)( xg
1)( xg
1)( xg
w
1
w
1
Maxmize margin
w
2
14. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
15
18. Deep subtrees are not very important
面子
暗順暗順 暗刻
depth
)10(
19
19.
11 22
),(),( 2121
t tNn Nn
t nnttK
F
i
ii
fl
nInInn i
1
21
)(
21 )()(),(
},,,{ 21 F
fffF
0
1
)(nIi
tN
)( ifl
Set of nodes in tree t
Subtree set
Depth of subtree fi
otherwise
If fi is rooted at node n
20
20. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
21
21. SVM is just a 2-class classifier
◦ How learn to rank
If you want to know ranks of three moves…
Order classifier ( > or < )
),(
),(
),(
32
31
21
mm
mm
mm
32
31
21
mm
mm
mm
213 mmm
Rank
Input data -> Pairs of moves
22
22. One training example has two tree instances
Define kernel function for relative order
r
i
l
ii tte ,
),(),(),(),(),( 2121212121
lr
t
rl
t
rr
t
ll
ttr ttKttKttKttKeeK
Classify “tl > tr” and “ tl< tr”
Label +1 when tl > tr
Label -1 when tl < tr
24
23. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
25
24. 1. Experiment of proposed method
2. Error analysis
3. Comparison with related work
4. Practical player
26
26. Learn from tsumo positions in expert records
◦ “Offensive” positions only
Nobody declares “li-zhi”
Nobody calls 3 or more “chi”, “pon” or “kan”
◦ Using records of Totugeki Tohoku
~285 games (~13,000 training positions)
Evaluation
◦ Accuracy rates of trained classifiers
Are expert moves ranked as the bests ?
◦ 4-fold cross validation
28
32. Core2 Duo 1.06GHz
91819 support vectors
700ms for classification of one tree pair
7 seconds for deciding one move
◦ 4 seconds in dual threading
◦ Good enough for playing against human players
36
33. 1. Introduction
2. Related work
3. Proposed method
◦ SVM with kernels
◦ Tree kernels in mahjong
◦ Learning to rank using SVM
4. Experiment
5. Conclusion
37
34. Classified ranks of moves with tree kernels
◦ Possible with simple input
57% accuracy
◦ Despite the lack of information of field and
opponents
◦ Increasing…
Fine accuracy with permissible cost
38
35. Classification analysis
◦ Positions that linear combinations cannot classify
Refine tree structure
Other information
◦ Hands information with other kernels
String kernels
◦ Information of field and opponents
Add as linear combinations or other kernels
Heavy computing cost
◦ Classification time increases with a number of training
positions
◦ Indispensable in other games
39
