傅立叶域中的变量消去法
Variable Elimination in the Fourier Domain
摘要：
以紧凑形式表示复杂高维概率分布的能力是图形模型领域的关键见解之一。因子表示在机器学习中无处不在，并带来了重大的计算优势。我们探讨了一种不同类型的紧凑表示的基础上离散傅立叶表示，补充经典的方法的基础上的条件独立性。我们发现，一个大类的概率图形模型有一个紧凑的傅立叶表示。这一理论结果为近似概率分布开辟了一条全新的途径。我们证明了这种方法的意义，将其应用到变量消除算法。与传统的桶表示和其他近似推理算法相比，我们得到了显著的改进。
英文摘要：
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.
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