Reasoning with BKBs - Algorithms and complexity

Bayesian Knowledge Bases (BKB) are a rule-based probabilistic model that extends the well-known Bayes Networks (BN), by naturally allowing for context-specific independence and for cycles in the directed graph. We present a semantics for BKBs that facilitate handling of marginal probabilities, as well as finding most probable explanations. Complexity of reasoning with BKBs is NP hard, as for Bayes networks, but in addition, deciding consistency is also NP-hard. In special cases that problem does not occur. Computation of marginal probabilities in BKBs is another hard problem, hence approximation algorithms are necessary - stochastic sampling being a commonly used scheme. Good performance requires importance sampling, a method that works for BKBs with cycles is developed.