In this paper, we formulate the problem of learning an Implicit Generative Model (IGM) as minimizing the expected distance between characteristic functions. Specifically, we match the characteristic functions of the real and generated data distributions under a suitably-chosen weighting distribution. This distance measure, which we term as the characteristic function distance (CFD), can be (approximately) computed with linear time-complexity in the number of samples, compared to the quadratic-time Maximum Mean Discrepancy (MMD). By replacing the discrepancy measure in the critic of a GAN with the CFD, we obtain a model that is simple to implement and stable to train; the proposed metric enjoys desirable theoretical properties including continuity and differentiability with respect to generator parameters, and continuity in the weak topology. We further propose a variation of the CFD in which the weighting distribution parameters are also optimized during training; this obviates the need for manual tuning and leads to an improvement in test power relative to CFD. Experiments show that our proposed method outperforms WGAN and MMD-GAN variants on a variety of unsupervised image generation benchmark datasets.

本文提出了一种基于特征函数距离（Characteristic Function Distance）的新颖的隐式生成模型评价方法，可用于无监督图像生成，并在实验中表现出优于WGAN和MMD-GAN变体的性能。

深度隐式生成建模的特征函数方法