ICS-280, Current Topics in Automated Reasoning, Spring 2003

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?