Variational Laplace Autoencoders
This addresses challenges in variational inference for deep generative models, offering a more expressive and accurate approach, though it appears incremental as it builds on existing autoencoder frameworks.
The paper tackled the limited posterior expressiveness and amortization error in variational autoencoders by proposing Variational Laplace Autoencoders, which use a Laplace approximation to enhance posterior expressiveness and reduce error, achieving significant performance improvements on datasets like MNIST, Omniglot, Fashion-MNIST, SVHN, and CIFAR10 compared to other methods.
Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized Gaussian assumption and (2) the amortization error of the inference model. We present a novel approach that addresses both challenges. First, we focus on ReLU networks with Gaussian output and illustrate their connection to probabilistic PCA. Building on this observation, we derive an iterative algorithm that finds the mode of the posterior and apply full-covariance Gaussian posterior approximation centered on the mode. Subsequently, we present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models. Based on the Laplace approximation of the latent variable posterior, VLAEs enhance the expressiveness of the posterior while reducing the amortization error. Empirical results on MNIST, Omniglot, Fashion-MNIST, SVHN and CIFAR10 show that the proposed approach significantly outperforms other recent amortized or iterative methods on the ReLU networks.