Probabilistic inference is a key computational challenge in statistical machine learning and artificial intelligence. The ability to represent complex high dimensional probability distributions in a compact form is the most important insight in the field of graphical models. In this paper, we explore a novel way to exploit compact representations of high-dimensional probability distributions in approximate probabilistic inference algorithms. Our approach is based on discrete Fourier Representation of weighted Boolean Functions, complementing the classical method to exploit conditional independence between the variables. 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 and comparing the results with the bucket representation and other approximate inference algorithms, obtaining very encouraging results.

本文研究在机器学习中广泛使用的图形模型中，一种基于离散傅里叶变换的紧凑表示方法，以及在这种表示方法下的概率分布的逼近方法。我们展示了这个理论结果的应用，并证明了它相对于传统的表示方法和其他逼近算法的显著优势。

傅里叶域的变量消除