1. The document proposes a regular quotient score for Bayesian network structure learning that allows for more efficient branch-and-bound search compared to the existing BDeu score. 2. The existing BDeu score violates regularity, meaning that Markov equivalent structures do not necessarily share the same BDeu score. 3. The authors propose a regular quotient score based on Jeffreys' prior that satisfies regularity, ensuring Markov equivalent structures share the score, enabling more efficient searching during branch-and-bound learning of Bayesian network structures.

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