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. Keywords: Variational Auto-Encoder; Generative model; Sobolev spaces; Radon Sobolev Variational Auto-Encoder;
翻译:基因变异模型的质量(如生成对抗网络和变异自动编码器)在很大程度上取决于概率距离的选择。 但是,一些流行的量度,如瓦瑟斯坦或剪切的瓦瑟斯坦距离、詹森-沙农差异、库尔背-利贝尔差异、缺乏方便的特性,如(eodesic)凝结性、快速评估等等。为了解决这些缺陷,我们引入了具有内在共性的距离等级。我们调查了与一些已知范式的关系(允许距离-拉登距离的同义词-再生产内核间距、能源距离 )。 距离显示具有快速执行功能,并包含在适应性自动变异电动自动电解器中,称为Radon Sobolev自动电解(RS-VAE),在标准基因变异基因数据集中产生高质量的结果。 Keywords:Variational-Autocoder; Genementalimedal;Sobolevelev;Radon Soboleval Variation;