We propose a semi-supervised generative model, SeGMA, which learns a joint probability distribution of data and their classes and is implemented in a typical Wasserstein autoencoder framework. We choose a mixture of Gaussians as a target distribution in latent space, which provides a natural splitting of data into clusters. To connect Gaussian components with correct classes, we use a small amount of labeled data and a Gaussian classifier induced by the target distribution. SeGMA is optimized efficiently due to the use of the Cramer–Wold distance as a maximum mean discrepancy penalty, which yields a closed-form expression for a mixture of spherical Gaussian components and, thus, obviates the need of sampling. While SeGMA preserves all properties of its semi-supervised predecessors and achieves at least as good generative performance on standard benchmark data sets, it presents additional features: 1) interpolation between any pair of points in the latent space produces realistically looking samples; 2) combining the interpolation property with disentangling of class and style information, SeGMA is able to perform continuous style transfer from one class to another; and 3) it is possible to change the intensity of class characteristics in a data point by moving the latent representation of the data point away from specific Gaussian components.

中文翻译：

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SeGMA：半监督高斯混合自编码器

我们提出了一个半监督生成模型 SeGMA，它学习数据及其类的联合概率分布，并在典型的 Wasserstein 自动编码器框架中实现。我们选择高斯混合作为潜在空间中的目标分布，这提供了数据到集群的自然分裂。为了将高斯分量与正确的类别连接起来，我们使用了少量标记数据和由目标分布诱导的高斯分类器。由于使用 Cramer-Wold 距离作为最大平均差异惩罚，SeGMA 得到了有效优化，这产生了球形高斯分量混合的封闭形式表达式，因此不需要采样。虽然 SeGMA 保留了其半监督前辈的所有属性，并且在标准基准数据集上至少实现了同样良好的生成性能，但它提供了额外的功能：1) 潜在空间中任意一对点之间的插值产生逼真的样本；2) 将插值特性与类和样式信息的解开相结合，SeGMA 能够执行从一个类到另一个类的连续样式转换；3) 可以通过将数据点的潜在表示从特定的高斯分量移开来改变数据点中类特征的强度。2) 将插值特性与类和样式信息的解开相结合，SeGMA 能够执行从一个类到另一个类的连续样式转换；3) 可以通过将数据点的潜在表示从特定的高斯分量移开来改变数据点中类特征的强度。2) 将插值特性与类和样式信息的解开相结合，SeGMA 能够执行从一个类到另一个类的连续样式转换；3) 可以通过将数据点的潜在表示从特定的高斯分量移开来改变数据点中类特征的强度。