Ideas for Research Projects
- w-cutset: Investigate approximate algorithms and properties for finding a w-cutset.
- Convert any integer programming problem to a relational constraint optimization that can interface through REES with all our algorithms.
- Develop an object oriented language for expressing constraint problems such as the Object oriented language of Pfeffer and Koller for probabilistc problems.
- LEARNING: Read Rish Survey about learning, Read abut EM, Read Russel, Koller et. Al on learning.
- Investigating the learning EM algorithm with a stronger inference component than greedy inside EM. One can start with learning HMM. Can we improve learning HMM in some way by more advance inference?
- Develop a one iteration learning algorithms that replace EM:
Complete each tuple using inference, then count the tuples giving each completed tuple its weight based on the computed probability. Is this a single iteration of EM?
- Algorithms for MAP applied to HMM's. Approximate MAP and incorporate in EM. Currently the expected counts are computed separately for every family. Alternative: compute expected completions per tuple, and only then take expected counts.
- Is there any relationship between EM and iterative belief propagation for MAP?
- Develop algorithms for MAP.
- Adapt search algorithms to MAP.
- Aanalyze MAP for trees.
- Develop iterative belief propagation for MAPs
- General search with caching simulating variable-elimination. Apply the idea of backtracking with no-good learning to any Look at Bacchus paper for the case of belief. Extend to optimization, either for MAX-CSP or for MPE first.
- Apply approximate inference with local search + iterative propagation as done by Pinkas and Dechter. Apply to optimization in general, to MPE and MAP.
- Develop Branch and bound for finding M-best solutions. Can we develop upper-bounds using mini-bucket for the ith solution and use it?