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：精确计算分区函数被认为是不可解的，因此需要近似推断技术。现有的近似推断方法在许多基准测试中收敛速度缓慢。控制精度-复杂度平衡在许多这些方法中也是非常棘手的。我们提出了一个新颖的增量构建推理-近似 (IBIA) 框架，用于近似推断，解决了这些问题。在这个框架中，概率图模型被转换成具有有界团大小的一系列团树森林 (SCTF)。我们表明，SCTF 可以用于高效地计算分区函数。我们提出了两个新算法，用于构建 SCTF，并证明了它们的正确性。第一个算法是用于增量构建 CTF 的算法，保证给出一个具有有界团大小的有效 CTF。第二个算法是一种近似算法，它以校准的 CTF 作为输入，将一组具有减小团大小的有效和校准的 CTF 作为输出。我们使用最近的 UAI 竞赛中的几组基准集来评估我们的方法，结果显示了良好的精度和有竞争力的运行时间。