论文标题
空间蒙特卡洛整合的概括
A Generalization of Spatial Monte Carlo Integration
论文作者
论文摘要
空间蒙特卡洛整合（SMCI）是标准蒙特卡洛整合的扩展，并且可以以高精度对马尔可夫随机场的期望进行近似。将SMCI应用于成对玻尔兹曼机器（PBM）学习，其结果优于某些现有方法的结果。可以更改SMCI的近似水平，并证明SMCI的高阶近似在统计学上比低阶近似更准确。但是，如先前的研究所提出的SMCI受到了阻止将高阶方法应用于密集系统的限制。 这项研究做出了两种不同的贡献，如下所示。提出了SMCI的概括（称为广义SMCI（GSMCI）），从而可以放松上述限制。此外，证明了GSMCI的统计精度。这是这项研究的第一个贡献。提出了一种基于SMCI的新PBM学习方法，该方法是通过组合SMCI和持续的对比分歧来获得的。提出的学习方法大大提高了学习的准确性。这是这项研究的第二个贡献。
Spatial Monte Carlo integration (SMCI) is an extension of standard Monte Carlo integration and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, with superior results to those from some existing methods. The approximation level of SMCI can be changed, and it was proved that a higher-order approximation of SMCI is statistically more accurate than a lower-order approximation. However, SMCI as proposed in the previous studies suffers from a limitation that prevents the application of a higher-order method to dense systems. This study makes two different contributions as follows. A generalization of SMCI (called generalized SMCI (GSMCI)) is proposed, which allows relaxation of the above-mentioned limitation; moreover, a statistical accuracy bound of GSMCI is proved. This is the first contribution of this study. A new PBM learning method based on SMCI is proposed, which is obtained by combining SMCI and the persistent contrastive divergence. The proposed learning method greatly improves the accuracy of learning. This is the second contribution of this study.
