Learning Bayesian Networks Under Sparsity Constraints: A Parameterized Complexity Analysis

We study the problem of learning structure an optimal Bayesian network when additional constraints are posed on or its moralized graph. More precisely, we consider constraint that graph close, in terms vertex edge deletions, to a sparse class Π. For example, show whose has deletion distance at most k from with maximum degree 1 can be computed polynomial time is constant. This extends previous work gave algorithm such running for edgeless graphs. then further extensions improvements presumably impossible. networks where have 2 connected components size c, c ≥ 3, NP-hard. Finally, edges no f(k) · |I|O(1)-time and that, contrast, arcs 2O(k) |I|O(1) |I| total input size.