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（即包含所有在忠实假设下精确结构学习算法的约束型算法家族），我们定义了局部化自然结构学习算法（LoNS）。同时给出了LoNS一致性的充要假设集，该假设可视为受限忠实假设的严格松弛条件。我们提出了一种指数时间复杂度的实用LoNS算法，并与现有相关结构学习算法（即PC/SGS算法及近年提出的Sparsest Permutation算法）进行对比。此外还提供了仿真研究。