Variational Laplace Autoencoders
arXiv:2211.17267
Abstract
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.
arXiv commentPublished in ICML 2019
References in corpus (11)
- Auto-Encoding Variational Bayes
- Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
- Stochastic Backpropagation and Approximate Inference in Deep Generative Models
- DRAW: A Recurrent Neural Network For Image Generation
- On the Number of Linear Regions of Deep Neural Networks
- A Recurrent Latent Variable Model for Sequential Data
- A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music
- Auxiliary Deep Generative Models
- Inference Suboptimality in Variational Autoencoders
- Iterative Amortized Inference
- On the challenges of learning with inference networks on sparse, high-dimensional data