Heuristic search

AND/OR Branch-and-Bound search

Kustaa Kangas

October 17, 2013

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 1 / 57

AND/OR search for probabilistic inference

Radu Marinescu, Rina Dechter, 2009

AND/OR Branch-and-Bound Search for Combinatorial Optimization inGraphical Models

1 Bayesian networks

2 Most Probable Explanation problem

3 OR search

4 AND/OR search (with Branch-and-Bound)

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 2 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 3 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 4 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 5 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 6 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 7 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 8 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 9 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 10 / 57

OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 11 / 57

Structural independencies

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 12 / 57

Structural independencies

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 13 / 57

Structural independencies

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 14 / 57

Structural independencies

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 15 / 57

Pseudo tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 16 / 57

Pseudo tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 17 / 57

Pseudo tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 18 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 19 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 20 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 21 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 22 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 23 / 57

AND/OR search tree

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 24 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 25 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 26 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 27 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 28 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 29 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 30 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 31 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 32 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 33 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 34 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 35 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 36 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 37 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 38 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 39 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 40 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 41 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 42 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 43 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 44 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 45 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 46 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 47 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 48 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 49 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 50 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 51 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 52 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 53 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 54 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 55 / 57

AND/OR search

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 56 / 57

Conclusion

The MPE an be formalized as a search problem.

OR search instantiates variables sequentially.

AND/OR search splits into independent subproblems.

Both search spaces may be pruned with Branch-and-Bound.

We didn’t cover

Heuristic functions

How to find pseudo trees?

Questions?

K. Kangas () Heuristic search AND/OR Branch-and-Bound search October 17, 2013 57 / 57