Automorphism Groups of Graphical Models and Lifted Variational Inference
Automorphism Groups of Graphical Models and Lifted Variational Inference
复制标题
图模型的自同构群和提升变分推理
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Sebastian Riedel
中科院分区：
文献类型：
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作者：
H. Bui;Tuyen N. Huynh;Sebastian Riedel
利用群作用理论，我们首先引入指数族或图模型的自同构群的概念，从而形式化概率模型对称性的一般概念。该自同构群为一般指数族中的提升推理提供了精确的数学框架。其群作用将随机变量和特征函数集划分为具有相同边际和期望的等效类（称为轨道）。然后，推理问题被有效地简化为计算每个类别的边际或期望的问题，从而避免了处理每个单独变量或特征的需要。我们证明了这个通用框架在提升 MAP 推理的两类变分近似方面的有用性：局部 LP 松弛和具有循环约束的局部 LP 松弛；后者产生第一个提升的推论，其运行范围比局部约束更严格。初步实验结果表明，具有循环约束的提升 MAP 推理实现了最先进的性能，获得了比局部逼近更好的目标函数值，同时保持相对高效。
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general exponential family. Its group action partitions the set of random variables and feature functions into equivalent classes (called orbits) having identical marginals and expectations. Then the inference problem is effectively reduced to that of computing marginals or expectations for each class, thus avoiding the need to deal with each individual variable or feature. We demonstrate the usefulness of this general framework in lifting two classes of variational approximation for MAP inference: local LP relaxation and local LP relaxation with cycle constraints; the latter yields the first lifted inference that operate on a bound tighter than local constraints. Initial experimental results demonstrate that lifted MAP inference with cycle constraints achieved the state of the art performance, obtaining much better objective function values than local approximation while remaining relatively efficient.