Learning Optimal Priors for Task-Invariant Representations in Variational Autoencoders

The variational autoencoder (VAE) is a powerful latent variable model for unsupervised representation learning. However, it does not work well in case of insufficient data points. To improve the performance in such situations, the conditional VAE (CVAE) is widely used, which aims to share task-invariant knowledge with multiple tasks through the task-invariant latent variable. In the CVAE, the posterior of the latent variable given the data point and task is regularized by the task-invariant prior, which is modeled by the standard Gaussian distribution. Although this regularization encourages independence between the latent variable and task, the latent variable remains dependent on the task. To reduce this task-dependency, the previous work introduced an additional regularizer. However, its learned representation does not work well on the target tasks. In this study, we theoretically investigate why the CVAE cannot sufficiently reduce the task-dependency and show that the simple standard Gaussian prior is one of the causes. Based on this, we propose a theoretical optimal prior for reducing the task-dependency. In addition, we theoretically show that unlike the previous work, our learned representation works well on the target tasks. Experiments on various datasets show that our approach obtains better task-invariant representations, which improves the performances of various downstream applications such as density estimation and classification.