变量消去法及其在张量计算中的应用
An Advance on Variable Elimination with Applications to Tensor-Based Computation
摘要：
我们提出了新的结果，经典算法的变量消除，这是许多算法的基础，包括概率推理。结果涉及到利用函数依赖关系，允许一个执行推理和学习有效的模型，具有非常大的树宽。这一进步的亮点在于，它使用标准（密集）因子，而不需要稀疏因子或基于常用知识汇编的技术。这是重要的，因为它允许使用张量和它们的操作直接实现改进的变量消除算法，导致非常有效的实现，特别是在学习模型参数时。此外，所提出的技术不需要了解特定的函数依赖关系，只需要知道它们存在，因此可以在学习这些依赖关系时使用。我们说明了我们提出的算法的有效性，通过将贝叶斯网络查询编译成张量图，然后使用张量计算的标准工具从标记数据中学习它们的参数。
英文摘要：
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference and learning efficiently on models that have very large treewidth. The highlight of the advance is that it works with standard (dense) factors, without the need for sparse factors or techniques based on knowledge compilation that are commonly utilized. This is significant as it permits a direct implementation of the improved variable elimination algorithm using tensors and their operations, leading to extremely efficient implementations especially when learning model parameters. Moreover, the proposed technique does not require knowledge of the specific functional dependencies, only that they exist, so can be used when learning these dependencies. We illustrate the efficacy of our proposed algorithm by compiling Bayesian network queries into tensor graphs and then learning their parameters from labeled data using a standard tool for tensor computation.
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