Exact computation of the partition function is known to be intractable, necessitating approximate inference techniques. Existing methods for approximate inference are slow to converge for many benchmarks. The control of accuracy-complexity trade-off is also non-trivial in many of these methods. We propose a novel incremental build-infer-approximate (IBIA) framework for approximate inference that addresses these issues. In this framework, the probabilistic graphical model is converted into a sequence of clique tree forests (SCTF) with bounded clique sizes. We show that the SCTF can be used to efficiently compute the partition function. We propose two new algorithms which are used to construct the SCTF and prove the correctness of both. The first is an algorithm for incremental construction of CTFs that is guaranteed to give a valid CTF with bounded clique sizes and the second is an approximation algorithm that takes a calibrated CTF as input and yields a valid and calibrated CTF with reduced clique sizes as the output. We have evaluated our method using several benchmark sets from recent UAI competitions and our results show good accuracies with competitive runtimes.

翻译：摘要：精确计算配分函数已知是棘手的，因此需要近似推理技术。现有近似推理方法在许多基准测试中收敛缓慢，且其中多数方法在精度-复杂度权衡的控制上也颇具挑战。我们提出了一个新颖的增量构建-推理-近似（IBIA）框架来解决这些问题。在该框架中，概率图模型被转换为具有有界团大小的团树森林序列（SCTF）。我们证明SCTF可用于高效计算配分函数。我们提出了两个新算法用于构建SCTF，并证明了二者的正确性。第一个是CTF增量构建算法，保证生成具有有界团大小的有效CTF；第二个是近似算法，以校准后的CTF为输入，输出团大小缩减的有效且校准的CTF。我们使用近期UAI竞赛中的多个基准数据集评估了该方法，结果显示本方法在具有竞争力的运行时间下取得了良好的精度。