Efficient Bayesian Network Structure Learning via Parameterized Local Search on Topological Orderings

In Bayesian Network Structure Learning (BNSL), we are given a variable set and parent scores for each aim to compute DAG, called network, that maximizes the sum of scores, possibly under some structural constraints. Even very restricted special cases BNSL computationally hard, and, thus, in practice heuristics such as local search used. typical algorithm, solution ask whether there is better within pre-defined neighborhood solution. We study ordering-based search, where described via topological ordering variables. show ordering, can an optimal DAG whose inversion distance r subexponential FPT time; parameter allows balance between quality running time algorithm. This bound be achieved without any constraints all expressed weights associated with set. other modification operations on orderings, algorithms unlikely. also outline limits by showing it cannot used common moralized graph network.