Laplacian Autoencoders for Learning Stochastic Representations
This work addresses the need for reliable uncertainty estimates in representation learning, which is crucial for evaluating stability in applications like data analysis and machine learning, though it appears incremental as it builds on existing autoencoder methods.
The authors tackled the problem of poorly calibrated uncertainty estimates in unsupervised representation learning by introducing a Bayesian autoencoder trained with a novel variational lower-bound and a scalable Hessian approximation, resulting in well-calibrated uncertainties and improved performance on downstream tasks.
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.