The Tilted Variational Autoencoder: Improving Out-of-Distribution Detection

A problem with using the Gaussian distribution as a prior for the variational autoencoder (VAE) is that the set on which Gaussians have high probability density is small as the latent dimension increases. This is an issue because VAEs try to attain both a high likelihood with respect to a prior distribution and at the same time, separation between points for better reconstruction. Therefore, a small volume in the high-density region of the prior is problematic because it restricts the separation of latent points. To ameliorate this, we propose a simple generalization of the Gaussian distribution, called the tilted Gaussian, which has a maximum probability density occurring on a sphere instead of a single point. The tilted Gaussian has exponentially more volume in high-density regions than the standard Gaussian as a function of the distribution dimension. We empirically demonstrate that this simple change in the prior distribution improves VAE performance on the task of detecting unsupervised out-of-distribution (OOD) samples. We also introduce a new OOD testing procedure, called the Will-It-Move test, where the tilted Gaussian achieves remarkable OOD performance.