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Transcript
“Lost in the Middle of
Nowhere”
Graduate Student Presentation
M. J. Gravier
Learning Bayesian
Network Structure
from Distributed Data
R. Chen, K. Sivakumar, H. Kargupta
SIAM International Conference on Data Mining 2003
Overview
• What is a Bayesian network?
• What problem is addressed?
• What is the contribution?
Bayesian Networks
• “...state-of-the-art representation
of probabilistic knowledge.”
• Graphical diagrams
• Probabilistic degrees of
dependency
• Efficient representation of a joint
probability distribution
Sun-Me Lee and Patricia Abbott, “Bayesian networks for knowledge
discovery in large datasets: basics for nurse researchers,” Journal of
Biomedical Informatics, 36 (2003):389-399.
Simple Bayesian Network
Day after rock
concert (X1)
Poor exam
grade (X2)
Mega
headache (X3)
“Structure Learning”: discovering relationships by
- a dependence analysis method (constraint satisfaction
problem, often based on hypothesis testing)
- a search and score method (basically an optimization
problem)
Advantages of BN
•
•
•
•
•
Domain expert knowledge
Simple to understand
Captures interactions
Flexible re: missing information
Less influenced by sample size
Disadvantages of BN
• Need conditional probabilities
• Lack of software
• Computational complexity
Typical Centralized Data
Site 2
Site 1
Database
Site 5
Site 3
Site 4
What if its Decentralized?
How do you create your
Bayesian network model
in this environment?
Different data at each site
Site 2
Site 1
Site 5
Site 3
Issues:
- variable data can all be in one site
Site 4
- variable data may be in two or more sites
- bandwidth
Collective Learning
1.
2.
3.
4.
Local Learning
Sample selection
Cross learning
Combination of the results
1. Local Learning
• Local variable: since all the
information is available locally, the
normal local scoring method
works
• But what about non-local
variables?
Cross Variables
• Some local and some non-local
parents
– local links can be found
– problem with cross links
Ulocal Ylocal instead of
Ulocal Znon-localYlocal
U
Z
Y
Site 2
Site 1
2. Sample Selection
• Rank-base local models
– low probabilities evidence of cross
relationships
• Send “keys” for models ranked
below threshold ρ from each site
to a central site
3. Cross Learning
• Keys from step 2 used to create a
BN of cross relationships
• ρ selection is critical
– try two different levels and retain
common cross links as a noise
reduction method
• Cross learning eliminates hidden
variables
4. Combination
• Combine local & cross load BNs
• All BNlocal assembled, then cross
links added with cross load BN
• Finds missing cross links for cross
variables
• Eliminates extra local links
(hidden variable problem)
Experimental Validation
• ALARM network
model
– on-line monitoring of
ICU patients
– widely used BN
benchmark
• Characteristics
– 37 nodes
– 5 cross variables
– 15,000 samples
Experimental Results
• Learned correct structure
• All cross links detected
• ~10% of all samples transmitted
Conclusion
• Collective learning method
learned same BN as centralized
method
• Small data transmission
requirement
• First approach to learn BN
structure from heterogeneous
data
Questions?