Learning a Sparse Generative Non-Parametric Supervised Autoencoder

Abstract

This paper concerns the supervised generative non parametric autoencoder. Classical methods are based on variational non supervised autoencoders (VAE). Variational autoencoders encourage the latent space to fit a prior distribution, like a Gaussian. However, they tend to draw stronger assumptions for 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 uses the labels to compute the latent space. Thus we define a global criterion combining classification and reconstruction loss. In addition, we have proposed a ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,1</inf> regularization which has the advantage of sparsifying the network and 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 dataset MNIST and two biological datasets.