1. Irina Rish IBM T.J.Watson Research Center rish@us.ibm.com
Advances in Bayesian Learning Learning and Inference in Bayesian Networks
Irina Rish
IBM T.J.Watson Research Center

2. “Road map” Introduction and motivation: How to use them
What are Bayesian networks and why use them?
How to use them
Probabilistic inference
How to learn them
Learning parameters
Learning graph structure
Summary

3. Bayesian Networks P (lung cancer=yes | smoking=no, dyspnoea=yes ) = ?
X-ray
Bronchitis
Dyspnoea
P (lung cancer=yes | smoking=no, dyspnoea=yes ) = ?

4. Bayesian Networks: Representation
P(D|C,B)
P(B|S)
P(S)
P(X|C,S)
P(C|S)
Smoking
lung Cancer
Bronchitis
CPD:
C B D=0 D=1
X-ray
Dyspnoea
P(S, C, B, X, D)
= P(S) P(C|S) P(B|S) P(X|C,S) P(D|C,B)
Conditional Independencies
Efficient Representation

5. What are they good for? Diagnosis: P(cause|symptom)=?
Prediction: P(symptom|cause)=?
Classification: P(class|data)
Decision-making (given a cost function)
Medicine
Bio-informatics
Computer
troubleshooting
Stock market
Text
Classification
Speech
recognition

6. Example: Printer Troubleshooting

7. Bayesian networks: inference P(X|evidence)=?
P(s|d=1)
“Moral” graph S X D B C
P(s)P(c|s)P(b|s)P(x|c,s)P(d|c,b)= C B
P(c|s)P(x|c,s)P(d|c,b) X D
P(s)
P(b|s)
Variable Elimination
W*=4
”induced width” (max clique size)
Complexity:
Efficient inference: variable orderings, conditioning, approximations

8. “Road map” Introduction and motivation: How to use them
What are Bayesian networks and why use them?
How to use them
Probabilistic inference
Why and how to learn them
Learning parameters
Learning graph structure
Summary

9. Why learn Bayesian networks?
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……………….
Combining domain expert knowledge with data
Efficient representation and inference
Incremental learning: P(H) or
Handling missing data: < ?? > S C
Learning causal relationships:

10. Learning Bayesian Networks
Known graph C S B D X
P(S)
P(B|S)
P(X|C,S)
P(C|S)
P(D|C,B)
– learn parameters
Complete data:
parameter estimation (ML, MAP)
Incomplete data:
non-linear parametric
optimization (gradient descent, EM) C S B D X
Unknown graph
– learn graph and parameters
Complete data:
optimization (search
in space of graphs)
Incomplete data:
structural EM,
mixture models C S B D X

11. Learning Parameters: complete data
ML-estimate:
- decomposable! X C B
Multinomial
counts
MAP-estimate (Bayesian statistics)
Conjugate priors - Dirichlet
Equivalent sample size
(prior knowledge)

12. Learning Parameters: incomplete data
Non-decomposable marginal likelihood (hidden nodes)
S X D C B
<? >
<1 1 ? 0 1>
< ? ?>
<? ? 0 ? 1>
………
Data
S X D C B
………..
Expected
counts
Expectation
Inference:
P(S|X=0,D=1,C=0,B=1)
Initial parameters
Current model
Update parameters
(ML, MAP)
Maximization
EM-algorithm:
iterate until convergence

13. Learning graph structure
Find
NP-hard
optimization
Heuristic search:
Greedy local search
Best-first search
Simulated annealing
Complete data – local computations
Incomplete data (score
non-decomposable):
Structural EM C S B
Add S->B C S B C S B
Delete
S->B C S B
Reverse
S->B
Constrained-based methods
Data impose independence
relations (constraints)

14. Scoring functions: Minimum Description Length (MDL)
Learning  data compression
Other: MDL = -BIC (Bayesian Information Criterion)
Bayesian score (BDe) - asymptotically equivalent to MDL
< >
< ?? ??>
< ?? >
<?? ??>
……………….
DL(Data|model)
DL(Model)

15. Summary Bayesian Networks – graphical probabilistic models
Efficient representation and inference
Expert knowledge + learning from data
Learning:
parameters (parameter estimation, EM)
structure (optimization w/ score functions – e.g., MDL)
Applications/systems: collaborative filtering (MSBN), fraud detection (AT&T), classification (AutoClass (NASA), TAN-BLT(SRI))
Future directions: causality, time, model evaluation criteria, approximate inference/learning, on-line learning, etc.