Laplacian Autoencoders for Learning Stochastic Representations

Marco Miani, Frederik Rahbæk Warburg, Pablo Moreno-Muñoz, Nicki Skafte Detlefsen, Søren Hauberg

Keywords: Laplace Approximation, Bayesian Learning, Unsupervised Representation Learning

TL;DR: Bayesian Auto Encoders using a novel, online training procedure of the Laplace approximation

Abstract: Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In this work, we present a Bayesian autoencoder for unsupervised representation learning, which is trained using a novel variational lower-bound of the autoencoder evidence. This is maximized using Monte Carlo EM with a variational distribution that takes the shape of a Laplace approximation. We develop a new Hessian approximation that scales linearly with data size allowing us to model high-dimensional data. Empirically, we show that our Laplacian autoencoder estimates well-calibrated uncertainties in both latent and output space. We demonstrate that this results in improved performance across a multitude of downstream tasks.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2206.15078/code)