Download Causal Data Mining

Causal Data Mining
Richard Scheines
Dept. of Philosophy, Machine Learning, &
Human-Computer Interaction
Carnegie Mellon
1. Predictive Data Mining
Finding predictive relationships in data
– What feature of student behavior predicts learning
– Who will default on credit cards
– Who will get an “A” in your course
– Which HS students will do well at CMU
– Do students cluster by “learning style”
Causal Data Mining
Finding causal relationships in data
– What feature of student behavior causes learning
– What will happen when we make everyone take a
reading quiz before each class
– What will happen when we program our tutor to
intervene to give hints after an error
Predictive Data Mining
X1
X2
X3
. .
Xk
Y
1
1.7
28
M
. . 2.4
1
2
2.0
11
F
. . 1.1
0
3
1.9
17
F
. . 1.1
1
.
.
.
.
. . .
.
.
.
.
.
. . .
.
N
2.8
12
M
. . 1.8
0
Data Mining Search
Predictive Model
Y = f(X1, X2, …Xk)
Predictive Data Mining
Model Classes
1.
Simple Regression
2.
Locally Weighted Regression
3.
Logistic Regression
Predictive Model
4.
Neural Nets
Y = f(X1, X2, …Xk)
5.
Vector Support Machines
6.
Decision Trees
7.
Bayes Net
8.
Naïve Bayes Classifier
9.
Independent Components
Data Mining Search
10. Clustering
11. Etc.
Predictive Data Mining
Data Mining Search
Predictive Model under Constraints
Y = f(X1, X2, …Xk),
e.g., f  Additive functions
Predictive Data Mining
Data Mining Search
Predictive Model under Constraints
Y = f(X1, X2, …Xk),
Or
Probability Model under Constraints:
P(Y | X1, X2, …, Xk), where P  Gaussian, with mean 0
Predictive Data Mining
Decision Tree Search
P(Hosp.) = .78
Pos
>57
>1.4
X-Ray
Neg
.
Age
Lab2
 1.4
Lab2
 1.8
P(Hosp.) = .10
P(Hosp.) = .66
>1.8
 57
P(Hosp.) = .59
Lab1
>2.3
P(Hosp.) = .75
 2.3
P(Hosp.) = .05
Predictive Data Mining
≠
Causal Data Mining
Conditioning is not the same as intervening
P(Y | X1, X2, …, Xk)

P(Y | X1set, X2, …, Xk)
Causal Discovery
Statistical Data  Causal Structure
Data
Equivalence Class of
Causal Graphs
X1
X1
X1
X2
X2
X2
X3
Causal Markov Axiom
(D-separation)
X3
X3
Statistical
Inference
Discovery Algorithm
Independence
Relations
X1
Background Knowledge
- X2 before X3
- no unmeasured common causes
X3 | X2
Causal Discovery Software TETRAD IV
www.phil.cmu.edu/projects/tetrad
Full Semester Online Course in
Causal & Statistical Reasoning
Full Semester Online Course in
Causal & Statistical Reasoning
• Course is tooled to record certain events:
 Logins, page requests, print requests, quiz attempts, quiz
scores, voluntary exercises attempted, etc.
• Each event was associated with attributes:
 Time
 student-id
 Session-id
Printing and Voluntary Comprehension Checks: 2002
--> 2003
2002
2003
-.41
voluntary
questions
print
.75
.302
pre
quiz
print
-.16
voluntary
questions
-.08
pre
.353
.41
.323
.25
final
final
References
•
Causation, Prediction, and Search, 2nd Edition, (2000), by P. Spirtes, C. Glymour,
and R. Scheines ( MIT Press)
•
Causality: Models, Reasoning, and Inference, (2000), Judea Pearl, Cambridge
Univ. Press
•
Shih, B., Koedinger, K., & Scheines, R. (2008). A Response Time Model for
Bottom-Out Hints as Worked Examples. Proceedings of the First Educational
Data Mining Conference.
•
Shih, B., Koedinger, K., and Scheines, R. (2007) "Optimizing Student Models for
Causality." in Proceedings of the 13th International Conference on Artificial
Intelligence in Education.
•
Arnold, A., Beck, J., and Scheines, R. (2006). "Feature Discovery in the Context
of Educational Data Mining: An Inductive Approach." Proceedings of the
AAAI2006 Workshop on Educational Data Mining, Boston, MA.
•
Scheines, R., Leinhardt, G., Smith, J., and Cho, K. (2005) "Replacing Lecture with
Web-Based Course Materials, Journal of Educational Computing Research, 32, 1,
1-26.
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