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：配分函数的精确计算已知具有难解性，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，且许多方法在精度-复杂度权衡控制方面存在显著挑战。针对这些问题，我们提出了一种新颖的增量式构建-推理-近似（IBIA）框架。在该框架中，概率图模型被转换为具有有界团规模的团树森林序列（SCTF）。我们证明了SCTF可用于高效计算配分函数。我们提出了两种新算法用于构建SCTF，并证明了其正确性：第一种是增量式构建团树森林的算法，保证生成具有有界团规模的有效团树森林；第二种是近似算法，以已校准的团树森林为输入，输出规模缩小且仍保持有效性与校准性的团树森林。我们使用近期UAI竞赛的多个基准数据集进行了评估，结果表明该方法在保持良好精度的同时具有具有竞争力的运行时间。