1. Active Cost-sensitive Learning (Intelligent Test Strategies)
Charles X. Ling, PhD
Department of Computer Science
University of Western Ontario, Ontario, Canada
Joint work with Victor Sheng, Qiang Yang, …

2. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

3. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

4. Everything has a cost/benefit!
Materials, products, services
Disease, working/living condition, waiting, …
Happiness, love, life, …
Money, Sex and Happiness: An Empirical Study, by David G. Blanchflower & Andrew J. Oswald, in Journal The Scandinavian Journal of Economics. 106:3, Pages:
Lasting/happy marriage is worth about $100,000 in happiness
Utility-based learning: optimization; unifies many issues & is ultimate goal

5. Everything has a cost/benefit!
In medical diagnosis…
Tests have costs: temperature ($1), X-ray ($30), biopsy ($900)
Diseases have costs: flu ($100), diabetes (100k), cancer (108)
Misdiagnosis has (different) costs
Cost of false alarm ($500) << cost of missing a cancer ($500,000)
Doctors: balance the cost of tests and misdiagnosis
Our goal: to minimize the total cost
Many other similar applications…
Model this process
Cost-sensitive learning
Intelligent test strategies
Patient
Test 1
Test 2 …
Test n
Cancer?
(Cost) $1
$30
...
$900
FP/FN= 100/300k
001 39
Low
High 1
002 35
Med ?
003 42
New1 ?
Med …

6. Review of Previous Work
Cost-sensitive learning: a survey (Turney 2000)
Active research, also for imbalanced data problem
CS meta learning (wrapper): thresholding, sampling, weighting, …
CS learning algorithms. CSNB, our CS trees
…but all consider misclassification costs only
Some work considers test costs only
A few previous works consider both test costs and misclassification costs (Turney 1995, Zubek and Dietterich 2002, Lizotte et al 2003); all computationally expensive

7. Review of Previous Work
Active learning: actively seeking for extra info
Pool-based: a pool of unlabeled examples, which ones to label
Membership query: Is this instance positive?
Feature value acquisition
During training. But “missing is useful!”
During testing: our work
Human learning is active in many ways

8. Review of Previous Work
Diagnosis: wide applications in medicine, mechanical systems, software, …
Most previous AI-based diagnosis systems…
Manually built (partially)
Does not incorporate costs/benefit
Cannot actively suggest the processes
Our work: cost-sensitive and active; useful for diagnosis and policy setting

9. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

10. Cost-sensitive Decision Tree
Patient
Test 1
Test 2 …
Test n
Cancer?
(Cost) $1
$30
...
$900
FP/FN= 100/300k
001 39
Low
High 1
002 35
Med ?
003 42 1 T1 T6 T2 T3
Low
Med
<36
>=36 2 a c b
Advantages: tree structure, comprehensiblity
Objective: minimizing the total cost of tests and misclassification.

11. Attribute Splitting Criteria
Previous methods: C4.5 reduces the entropy (randomness), performs badly on cost sensitive tasks
New (ICML’04): we reduce the total expected cost E E3 E2 E1 1 2 3
Choose T such that E – (E1+E2+E3) is max C C3 C2 C1 1 2 3
Choose T such that C – (C1+C2+C3+C_Test) is max

12. Case Study: Heart Disease
Predict coronary artery disease
Class 0: less than 50% artery narrowing; Class 1: more than 50% artery narrowing
~300 patients, collected from hospitals
13 non-invasive tests on patients

13. 13 Tests (Heart Disease) Tests Costs Meaning age $1 age of the patient
sex cp
chest pain type
trestbps
resting blood pressure
chol
$7.27
cholesterol in mg/dl
fbs
$5.20
fasting blood sugar
restecg
$15.50
resting electrocardiography results
thalach
$102.90
maximum heart rate
thal
maximum heart rate reached
exang
$87.30
exercise induced angina
oldpeak
ST depression induced by exercise
slope
slope of the peak exercise ST segment ca
$100.90
number of major vessels colored by fluoroscopy

14. Cost-sensitive tree for Heart Disease1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
age
Naturally prefer tests with small cost
Balance cost and discriminating power
Local heart-failure specialist thinks this tree is reasonable.

15. Considering Group Discount
Tests
Costs
Meaning
age $1
age of the patient
sex cp
chest pain type
trestbps
resting blood pressure
chol
$7.27
cholesterol in mg/dl
fbs
$5.20
fasting blood sugar
restecg
$15.50
resting electrocardiography results
thalach
$102.90
maximum heart rate
thal
finishing heart rate
exang
$87.30
exercise induced angina
oldpeak
ST depression induced by exercise
slope
slope of the peak exercise ST segment ca
$100.90
number of major vessels colored by fluoroscopy
Discount: $2.10
Discount: $101.90
Discount: $86.30

16. Different trees without/with group discount1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age 1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
age
individual cost: $102.9
Before
After

17. Algorithm of Cost-sensitive Decision Tree
CSDT(Examples, Attributes, TestCosts)
If all examples are positive, return root with label=+
If all examples are negative, return root with label=-
If maximum cost reduction <0, return root with label according to min(PTP+ NFP, NTN+ PFN)
Let A be an attribute with maximum cost reduction
root  A
Update TestCosts if discount applies
For each possible value vi of the attribute A
Add a new branch A=vi below root
Segment the training examples Example_vi into the new branch
Call CSDT(examples_vi, Attributes-A, TestCosts) to build subtree

18. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

19. Three categories of intelligent test strategies
Patient
Test 1
Test 2 …
Test n
Cancer?
(Cost) $1
$30
...
$900
FP/FN= 100/300k
001 39
Low
High 1
002 35
Med ?
003 42 1 T1 T6 T2 T3
Low
Med
<36
>=36 2 a c b
New1 ? …
Three categories of intelligent test strategies
Sequential Test: one test, wait, … then predict
Single Batch Test: one batch of tests, then predict
Sequential Batch Test: batch 1, batch 2, … then predict
Minimize total cost of tests and misclassification, not trivial
Our methods: utilizing the minimum-cost tree structure

20. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

21. Sequential Test Use tree structure to guide test sequence
“Optimal” because tree is (locally) optimal

22. Sequential Test 4 1 2 3 thal ($102.9) fbs ($5.2) restecg ($15.5) sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age

23. Experimental Comparison
Using 10 datasets from UCI
No. of Attributes
No. of Examples
Class dist. (N/P)
Ecoli 6
332
230/102
Breast 9
683
444/239
Heart 8
161
98/163
Thyroid 24
2000
1762/238
Australia 15
653
296/357
Tic-tac-toe
958
332/626
Mushroom 21
8124
4208/3916
Kr-vs-kp 36
3196
1527/1669
Voting 16
232
108/124
Cars
446
328/118

24. Comparing Sequential Test
Eager learning: Sequential Test (OST) (ICML’04)
Lazy learning: Lazy Sequential Test (LazyOST) (TKDE’05)
Cost-sensitive Naïve Bayes (CSNB) (ICDM’04)

25. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

26. Single Batch Test Only one batch – not an easy task
If too few, important tests not requested; prediction is not accurate; total cost high
If too many, some tests are wasted; total cost high
The test example may not be classified by a leaf

27. Single Batch Test
Expected cost reduction: if a test is done, what are the possible outcomes and cost reduction
R(.): all reachable unknown nodes and leaves i j3 j2 j1 1 2 3

28. Single Batch Test A*-like search algorithm
Form a candidate list (L) and a batch list (B)
Choose a test with maximum positive expected cost reduction from L, add it to B
Update L: add all reachable unknowns to L
Efficient with tree structure
until expected cost reduction is 0

29. Single Batch Test
L = empty /* list of reachable and unknown attributes */
B = empty /* the batch of tests */
u = the first unknown attribute when classifying a test case
Add u into L
Loop
For each i L, calculate E(i):
E(i)= misc(i) – [c(i) ]
E(t) = max E(i) /* t has the maximum cost reduction */
If E(t) > 0 then add t into B, delete t from L, add r(t) into L
else exit Loop /* No positive cost reduction */
Until L is empty
Output B as the batch of tests

30. Single Batch Test 4 1 2 3 thal ($102.9) fbs ($5.2) restecg ($15.5) sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age ]

31. Single Batch Test 1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age
cp is unknown. cp has positive expected cost reduction. cp is added to the batch. cp’s reachable unknown nodes are added into the candidate list. ]

32. Single Batch Test 1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age
From the candidate list, choose one with maximum positive expected cost reduction. Add it to the batch, and update the candidate list. Repeat. After 7 steps, expected cost reduction is 0. ]

33. Single Batch Test Do all tests in the batch 4 1 2 3 thal ($102.9) fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age
Do all tests in the batch ]

34. Predict by internal node
Single Batch Test 1 2 3 4
thal
($102.9)
fbs
($5.2)
restecg
($15.5)
sex
($1)
chol
($7.27) cp
slope
($87.3)
thalach
age
Make a prediction. Some tests are wasted. ]
Predict by internal node

35. Comparing Single Batch Tests
Naïve Single Batch (NSB) (ICML’04)
Cost-sensitive Naïve Bayes Single Batch (CSNB-SB) (ICDM’04)
Greedy Single Batch (GSB) (TKDE’05)
Single Batch Test (OSB) (TKDE’05)

36. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

37. Sequential Batch Batch 1, batch 2, … , prediction
Must include the cost of waiting in tests
Wait cost of a batch: maximum wait cost in the batch
Less than the sum
Combines Sequential Test and Single Batch Test
If all waiting costs =0, it becomes Sequential Test
If all waiting costs very large, Single Batch

38. Sequential Batch The wait cost is derived from wait time
Test wait time in hours
age
sex cp
trestbps
chol
fbs
restecg
thalach
exang
oldpek
slope ca
thal
0.001
0.01 4
0.5 1

39. Sequential Batch Extending the Single Batch to include the batch cost
An additional constraint: cumulative ROI
No more batches!

40. Sequential Batch
Loop
L = empty /* list of reachable and unknown attributes */
B = empty /* the batch of tests */
u = the first unknown attribute when classifying a test case
Add u into L
For each i L, calculate E(i):
E(i)= misc(i) – [c(i) ]
E(t) = max E(i) /* t has the maximum cost reduction */
If E(t) > 0 & ROI increases then add t into B, delete t from L, add r(t) into L
else exit Loop /* No positive cost reduction */
Until L is empty
If (B is not empty) then
Output B as the current batch of tests; obtain their values at a cost
Classify the test example further, until encountering another unknown test
Else exit the first Loop

41. Comparing Sequential Batch Test

42. Outline Introduction Cost-sensitive decision trees Test strategies
Sequential Test
Single Batch Test
Sequential Batch Test
Conclusions and future work

43. Future Work Deal with different test examples differently
Consider more costs: acquiring new examples
If $10 for each new example, how many do I need?
For $10, tell me if this patient has cancer
If test is not accurate (e.g. 90%), how to build trees and how to do tests (will I do it again)?
From cost-sensitive trees, derive medical policy for expensive/risky or cheap/effective tests

44. Conclusions
Cost-sensitive decision tree: effective for learning with minimal total cost
Can be used to model learning from data with costs
Design and compare various test strategies
Sequential Test: one test, wait, …: low cost but long wait
Single Batch Test: one batch of tests: quick but higher cost
Sequential Batch Test: batch, wait, batch, …: best tradeoff
Our methods perform better than previous ones
Can be readily applied to real-world diagnoses

45. References
C.X. Ling, Q. Yang, J. Wang, and S. Zhang. Decision Trees with Minimal Costs. ICML'2004.
X. Chai, L. Deng, Q. Yang, and C.X. Ling. Test-Cost Sensitive Naive Bayes Classification. ICDM'2004.
C.X. Ling, S. Sheng, Q. Yang. “Intelligent Test Strategies for Cost-sensitive Decision Trees. IEEE TKDE, to appear, 2005.
S. Zhang, Z. Qin, C.X. Ling, S. Sheng. "Missing is Useful": Missing Values in Cost-sensitive Decision Trees. IEEE TKDE, to appear, 2005.
Turney, P.D Types of cost in inductive concept learning. Workshop on Cost-Sensitive Learning at ICML’2000.
Zubek, V.B., and Dietterich, T Pruning improves heuristic search for cost-sensitive learning. ICML’2002.
Turney, P.D Cost-Sensitive Classification: Empirical Evaluation of a Hybrid Genetic Decision Tree Induction Algorithm. JAIR, 2:
Lizotte, D., Madani, O., and Greiner R Budgeted Learning of Naïve-Bayes Classifiers. In Uncertainty in AI.