6. proposed Dynamic Programming framework:
• Finding the parent set of each variable
• Ordering the variables to avoid making loops
Silander-Milymaki (2006)
Part I
Part II
9. MDL with B&B (Suzuki ICML‘96)
Cut Rule
Computing this and
deeper can be saved
10. An optimal parent set contains at most log n variables
(Campos et.al, 2011)
11.
12.
13.
14. B&B Strategies for Maxmizing Posterior Probability for BDeu
(Campos et. al., 2011)
15. Problems
1. What is the exact formula for BD rather than BDeu?
2. How tight is the existing inequality?
3. At most how many variables the optimal parent set
contains for maximizing the posterior rather than
minimizing the description length?
20. Main (negative) result for the cutting rule for BD/BDeu
Theorem 2:
No bound for how many variables the optinal π(X) contains
(unlike log n for MDL)
22. Concluding Remarks
Learning BN with B&B for maximizing Posterior probability:
• Cutting Rule for BD (extension of the existing bound, Theorem 1)
• The obtained bound in Theorem 1 is so loose that no upper bound of
the cardinality of optimal parent sets unlike MDL (Theorem 2)
Future Work
• Tighter Bound for Theorem 1