Several approaches to graphically representing context-specific relations among jointly distributed categorical variables have been proposed, along with structure learning algorithms. While existing optimization-based methods have limited scalability due to the large number of context-specific models, the constraint-based methods are more prone to error than even constraint-based directed acyclic graph learning algorithms since more relations must be tested. We present an algorithm for learning context-specific models that scales to hundreds of variables. Scalable learning is achieved through a combination of an order-based Markov chain Monte-Carlo search and a novel, context-specific sparsity assumption that is analogous to those typically invoked for directed acyclic graphical models. Unlike previous Markov chain Monte-Carlo search methods, our Markov chain is guaranteed to have the true posterior of the variable orderings as the stationary distribution. To implement the method, we solve a first case of an open problem recently posed by Alon and Balogh. Future work solving increasingly general instances of this problem would allow our methods to learn increasingly dense models. The method is shown to perform well on synthetic data and real world examples, in terms of both accuracy and scalability.

翻译：针对联合分布的类别变量之间的上下文特定关系，已有多种图形表示方法及相应的结构学习算法被提出。现有基于优化的方法因上下文特定模型数量庞大而可扩展性有限；而基于约束的方法由于需要检验更多关系，甚至比基于约束的有向无环图学习算法更易产生误差。本文提出一种学习上下文特定模型的算法，可扩展至数百个变量。可扩展学习通过结合基于次序的马尔可夫链蒙特卡洛搜索与一种新颖的上下文特定稀疏性假设实现，该假设类似于通常在有向无环图模型中采用的假设。与以往的马尔可夫链蒙特卡洛搜索方法不同，本文提出的马尔可夫链能保证变量次序的真实后验分布为其平稳分布。为实现该方法，我们解决了Alon和Balogh近期提出的一个开放问题的首个特例。未来通过解决该问题日益一般的实例，可使我们的方法学习日益稠密的模型。实验表明，该方法在合成数据与真实案例中，在准确性与可扩展性方面均表现良好。