Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances.

Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances.

This thesis explores and compares different methods of optimizing queries in Bayesian networks. Bayesian networks are graph-structured models that model probabilistic variables and their influences on each other; a query poses the question of what probabilities certain variables assume, given observed values on certain other variables. Bayesian inference (calculating these probabilities) is known to be NP-hard in general, but good algorithms exist in practice. Inference optimization traditionally concerns itself with finding and tweaking efficient algorithms, and leaves the choice of algorithms' parameters, as well as the construction of inference-friendly Bayesian network models, as an exercise to the end user. This thesis aims towards a more systematic approach to these topics: We try to optimize the structure of a given Bayesian network for inference, also taking into consideration what is known about the kind of queries that are posed. First, we implement several automatic model modifications that should help to make a model more suitable for inference. Examples of these are the conversion of definitions of conditional probability distributions from table form to noisy gates, and divorcing parents in the graph. Second, we introduce the concepts of usage profiles and query interfaces on Bayesian networks and try to take advantage of them. Finally, we conduct performance measurements of the different options available in the used library for Bayesian networks, to compare the effects of different options on speedup and stability, and to answer the question of which options and parameters represent the optimal choice to perform fast queries in the end product. The thesis gives an overview of what issues are important to consider when trying to optimize an application's query performance in Bayesian networks, and when trying to optimize Bayesian networks for queries. The project uses the SMILE library for Bayesian networks by the University of Pittsburgh, and includes a case study on script-generated Bayesian networks for troubleshooting by Scania AB.