A Hybrid of Generative and Discriminative Models Based on the Gaussian-Coupled Softmax Layer

Generative models offer advantageous characteristics for classification tasks, such as the availability of unsupervised data and calibrated confidence. In contrast, discriminative models have advantages in terms of their potential to outperform their generative counterparts and the simplicity of their model structures and learning algorithms. In this article, we propose a method to train a hybrid of discriminative and generative models in a single neural network (NN), which exhibits the characteristics of both models. The key idea is the Gaussian-coupled softmax layer, which is a fully connected layer with a softmax activation function coupled with Gaussian distributions. This layer can be embedded into an NN-based classifier and allows the classifier to estimate both the class posterior distribution and the input data distribution. We demonstrate that the proposed hybrid model can be applied to semi-supervised learning and confidence calibration.