Learning A Sparse Generative Non-Parametric Supervised Autoencoder

This paper concerns the supervised generative non parametric autoencoder. Classical methods are based on variational autoencoders (VAe). Variational autoencoders encourage the latent space to fit a prior distribution, like a Gaussian. However, they tend to draw stronger assumptions form 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. Thus we define a global criterion combining classification and reconstruction loss. In addition, we have proposed a $\ell_{1,1}$ regularization which has the advantage of sparsifying the network improving the clustering. Finally we propose a tailored algorithm to minimize the criterion with constraint. We demonstrate the effectiveness of our method using the popular image datasets MNIST and two biological datasets.