1. A Simple and Effective Method for Incorporating Advice into Kernel Methods
Richard Maclin
University of Minnesota - Duluth
Jude Shavlik, Trevor Walker, Lisa Torrey
University of Wisconsin - Madison

2. The Setting Given Examples of classification/regression task
Advice from an expert about the task Do
Learn an accurate model
Knowledge-Based Classification/Regression

3. Advice goalie isn’t covering it and angleGoalieGCenter ≥ 25
IF goal center is close and
goalie isn’t covering it
THEN Shoot!
and
angleGoalieGCenter ≥ 25
IF distGoalCenter ≤ 15
THEN Qshoot(x) ≥ 0.9

4. Knowledge-Based Classification

5. + penalties for not following advice (hence advice can be refined )
Knowledge-Based Support Vector Methods [Fung et al., 2002, 2003 (KBSVM), Mangasarian et al., 2005 (KBKR)]
min size of model + C |s|
+ penalties for not following advice (hence advice can be refined )
such that
f(x) = y  s
+ constraints that represent advice
slack terms

6. Our Motivation KBKR adds many terms to opt. problem
Want accurate but more efficient method
Scale to a large number of rules
KBKR alters advice in somewhat hard to understand ways (rotation and translation)
Focus on a simpler method

7. Our Contribution – ExtenKBKR
Method for incorporating advice that is more efficient than KBKR
Advice defined extensionally rather than intensionally (as in KBKR)

8. Support Vector Machines

9. Knowledge-Based SVM
Also penalty
for rotation,
translation

10. Note, point from one class pseudo labeled with the other class
Our Extensional KBSVM
Note, point from one class pseudo labeled with the other class

11. Incorporating Advice in KBKR
Advice format
Bx ≤ d  f(x) ≥ 
IF distGoalCenter ≤ 15 and
angleGoalieGCenter ≥ 25
THEN Qshoot(x) ≥ 0.9

12. Linear Program with Advice
KBKR
min sum per action a
||w||1 + |b| + C|sa|
+ sum per advice k
1||zk||1+ 2 k
such that
for each action a
wax +ba = Qa(x)  sa
for each advice k
wk+BkTuk = 0  zk
-dT uk + k ≥ k – bk
ExtenKBKR
( / |Mk|) ||mk||1
Mk wk + bk + m ≥ k

13. Choosing Examples “Under” Advice
Training data – adds second label
more weight if labeled same
less if labeled differently
Unlabeled data – semi-supervised method
Generated data – but can be complex to generate meaningful data

14. Size of Linear Program Additional Items Per Advice Rule KBKR ExtenKBKR
Variables
E+1 Mk
Constraint Terms E2
E Mk
E – number of examples
Mk – number of examples per advice item
(expect Mk << E)

15. Artificial Data: Methodology
10 input variables
Two functions
f1 = 20x1x2x3x4 – 1.25
f2 = 5x5 – 5x2 + 3x6 – 2x4 – 0.5
Selected C, 1, 2,  with tuning set
Considered adding 0 or 5 pseudo points
Used Gaussian kernel

16. Artificial Data: Advice
IF x1 ≥ .7  x2 ≥ .7  x3 ≥ .7  x4 ≥ .7 THEN f1(x) ≥ 4
IF x5 ≥ .7  x2 ≤ .3  x6 ≥ .7  x4 ≤ .3 THEN f2(x) ≥ 5
IF x5 ≥ .6  x6 ≥ .6 THEN PREFER f2(x) TO f1(x) BY .1
IF x5 ≤ .3  x6 ≤ .3 THEN PREFER f1(x) TO f2(x) BY .1
IF x2 ≥ .7  x4 ≥ .7 THEN PREFER f1(x) TO f2 (x) BY .1
IF x2 ≤ .3  x4 ≤ .3 THEN PREFER f2(x) TO f1(x) BY .1

17. Error on Artificial Data

18. Time Taken on Artificial Data

19. RoboCup: Methodology Test on 2-on-1 BreakAway 13 tiled features
Average over 10 runs
Selected C, 1, 2,  with tuning set
Use linear model (tiled features for non-linearity)

20. ExtenKBKR twice as fast as KBKR in CPU cycles
RoboCup Performance
ExtenKBKR twice as fast as KBKR in CPU cycles

21. Related Work Knowledge-Based Kernel Methods
Fung et al., NIPS 2002, COLT 2003
Mangasarian et al., JMLR 2005
Maclin et al., AAAI 2005
Le et al., ICML 2006
Mangasarian and Wild, IEEE Trans Neural Nets 2006
Other Methods Using Prior Knowledge
Schoelkopf et al., NIPS 1998
Epshteyn & DeJong, ECML 2005
Sun & DeJong, ICML 2005
Semi-supervised SVMs
Wu & Srihari, KDD 2004
Franz et al., DAGM 2004

22. Future Work Label “near” examples to allow advice to expand
Analyze predictions for pseudo-labeled examples to determine how advice refined
Test on semi-supervised learning tasks

23. Conclusions ExtenKBKR
Key idea: sample advice (extensional definition) and train using standard methods
Empirically as accurate as KBKR
Empirically more efficient than KBKR
Easily adapted to other forms of advice

24. Acknowledgements
US Naval Research Laboratory grant N G002 (to RM)
DARPA grant HR (to JS)

25. Questions?