Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn the structure of the MRF, that is the neighbors of each node of the underlying graph. In this work, we start at a known near-optimal classical algorithm for this learning problem and develop a modified classical algorithm. This classical algorithm retains the run time and guarantee of the previous algorithm and enables the use of quantum subroutines. Adapting a previous quantum algorithm, the Quantum Sparsitron, we provide a polynomial quantum speedup in terms of the number of variables for learning the structure of an MRF, if the MRF has bounded degree.
翻译:Markov随机字段(MRFs)出现在机器学习和统计的许多问题中。从计算学习理论的角度来看,学习MRF的自然问题产生:从一个受限制的等级的MRF样本中,学习MRF的结构,即基图的每个节点的周边。在这项工作中,我们从一个已知的接近最佳的经典算法开始,以研究这个学习问题,并开发一个经修改的古典算法。这一古典算法保留了前算法的运行时间和保证,并允许使用量子路程。调整了以前的量子算法,即Quantum Sparsitron,我们提供了多数值加速,以变量的数量来学习MRF的结构,如果MRF具有约束度的话。