Uncertainty in Artificial Intelligence, August 12-15, 2017, Sydney, Australia.

1. B&B for Regular BNSL
Joe Suzuki (Osaka U.) & Jun Kawahara (Nara Sen)
BDeu will die today ! Do not miss !
UAI 2017 #78
1. Define Regularity of BNSL
2. BDeu is not Regular
3. Markov equivalent structures share not just BDeu but also quotient scores
4. Regular BNSL offers efficient B & B
5. Propose a regular quotient score

2. BNSL
Discrete

3. Scores

4. Conditional/Quotient Scores

5. Markov Equivalent Structures

6. For Markov equivalent structures to share the Conditional Score,
there should be δ> 0 s.t.
BDeu (Buntine, 1991)
α, β: # of values that X and Y take

7. Markov equivalent structures share any Quotient Score

8. B&B for BNSL

9. BDeu violates regularity
(Suzuki 2017)

10. Quotient + Jeffreys’ satisfies regularity

11. MDL is regular

15. The proposed B&B is more efficient than the existing one

16. Regular BNSL offers efficient B&B while BDeu does not