  By relaxing conditions for natural structure learning algorithms, a family of
constraint-based algorithms containing all exact structure learning algorithms
under the faithfulness assumption, we define localised natural structure
learning algorithms (LoNS). We also provide a set of necessary and sufficient
assumptions for consistency of LoNS, which can be thought of as a strict
relaxation of the restricted faithfulness assumption. We provide a practical
LoNS algorithm that runs in exponential time, which is then compared with
related existing structure learning algorithms, namely PC/SGS and the
relatively recent sparsest permutation algorithm. Simulation studies are also
provided.
