A Non-Parametric Supervised Autoencoder for discriminative and generative modeling

This paper deals with supervised discriminative and generative modeling. Classical methods are based on variational autoencoders or supervised variational autoencoders encourage the latent space to fit a prior distribution, like a Gaussian. However, they tend to make stronger assumptions on the data, often leading to higher asymptotic bias when the model is wrong. In this paper, we relax the parametric distribution assumption in the latent space and we propose to learn a non-parametric data distribution of the clusters in the latent space. The network encourages the latent space to fit a distribution learned with the labels instead of the parametric prior assumptions. We have built a network architecture that incorporates the labels into an autoencoder latent space to create discriminative and generative models. Thus we define a global criterion combining classification and reconstruction loss. In addition, we have proposed a 1,1 regularization which advantages are a faster convergence of the algorithm and an improvement of the clustering. Finally we propose a tailored algorithm to minimize the criterion with constraint. We demonstrate the effectiveness of our method on two popular image datasets (MNIST and Fashion MNIST) and two biological datasets.