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.

翻译：通过放宽自然结构学习算法的条件——这类算法包含所有在忠实性假设下精确的结构学习算法——我们定义了局部化自然结构学习算法（LoNS）。我们还为LoNS的一致性提供了一组必要且充分的假设条件，这可以被视为对受限忠实性假设的严格放宽。我们提出了一种实用的LoNS算法，其运行时间为指数级，并与相关的现有结构学习算法（即PC/SGS算法和相对较新的最稀疏排列算法）进行了比较。同时提供了仿真研究结果。