Turinici Gabriel
Université Paris Dauphine - PSL Research University CEREMADE, Place du Marechal de Lattre de Tassigny, Paris 75016, France.
Neural Netw. 2021 Sep;141:294-305. doi: 10.1016/j.neunet.2021.04.018. Epub 2021 Apr 22.
The quality of generative models (such as Generative adversarial networks and Variational Auto-Encoders) depends heavily on the choice of a good probability distance. However some popular metrics like the Wasserstein or the Sliced Wasserstein distances, the Jensen-Shannon divergence, the Kullback-Leibler divergence, lack convenient properties such as (geodesic) convexity, fast evaluation and so on. To address these shortcomings, we introduce a class of distances that have built-in convexity. We investigate the relationship with some known paradigms (sliced distances - a synonym for Radon distances - reproducing kernel Hilbert spaces, energy distances). The distances are shown to possess fast implementations and are included in an adapted Variational Auto-Encoder termed Radon-Sobolev Variational Auto-Encoder (RS-VAE) which produces high quality results on standard generative datasets.
生成模型（如生成对抗网络和变分自编码器）的质量在很大程度上取决于良好概率距离的选择。然而，一些流行的度量，如瓦瑟斯坦距离或切片瓦瑟斯坦距离、詹森 - 香农散度、库尔贝克 - 莱布勒散度，缺乏诸如（测地线）凸性、快速评估等便利性质。为了解决这些缺点，我们引入了一类具有内在凸性的距离。我们研究了与一些已知范式（切片距离——拉东距离的同义词——再生核希尔伯特空间、能量距离）的关系。结果表明，这些距离具有快速实现方式，并被纳入一种经过改进的变分自编码器，称为拉东 - 索伯列夫变分自编码器（RS - VAE），该编码器在标准生成数据集上产生高质量的结果。
