We study the problem of learning a Bayesian network (BN) of a set of
variables when structural side information about the system is available. It is
well known that learning the structure of a general BN is both computationally
and statistically challenging. However, often in many applications, side
information about the underlying structure can potentially reduce the learning
complexity. In this paper, we develop a recursive constraint-based algorithm
that efficiently incorporates such knowledge (i.e., side information) into the
learning process. In particular, we study two types of structural side
information about the underlying BN: (I) an upper bound on its clique number is
known, or (II) it is diamond-free. We provide theoretical guarantees for the
learning algorithms, including the worst-case number of tests required in each
scenario. As a consequence of our work, we show that bounded treewidth BNs can
be learned with polynomial complexity. Furthermore, we evaluate the performance
and the scalability of our algorithms in both synthetic and real-world
structures and show that they outperform the state-of-the-art structure
learning algorithms.

本研究开发了一种递归约束算法，能够高效地将结构性边缘信息引入学习贝叶斯网络 (BN) 的过程，并提供了该算法的理论保证，进一步表明有界树宽 BN 可以在不增加复杂度的情况下学习。