Learnable Explicit Density for Continuous Latent Space and Variational Inference

In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and inference. Second, we analyze the family of inverse autoregressive flows (inverse AF) and show that with further improvement, inverse AF could be used as universal approximation to any complicated posterior. Our analysis results in a unified approach to parameterizing a VAE, without the need to restrict ourselves to use factorial Gaussians in the latent real space.Comment: 2 figures, 5 pages, submitted to ICML Principled Approaches to Deep Learning worksho

To Regularize or Not To Regularize? The Bias Variance Trade-off in Regularized AEs

Regularized Auto-Encoders (RAEs) form a rich class of neural generative models. They effectively model the joint-distribution between the data and the latent space using an Encoder-Decoder combination, with regularization imposed in terms of a prior over the latent space. Despite their advantages, such as stability in training, the performance of AE based models has not reached the superior standards as that of the other generative models such as Generative Adversarial Networks (GANs). Motivated by this, we examine the effect of the latent prior on the generation quality of deterministic AE models in this paper. Specifically, we consider the class of RAEs with deterministic Encoder-Decoder pairs, Wasserstein Auto-Encoders (WAE), and show that having a fixed prior distribution, \textit{a priori}, oblivious to the dimensionality of the `true' latent space, will lead to the infeasibility of the optimization problem considered. Further, we show that, in the finite data regime, despite knowing the correct latent dimensionality, there exists a bias-variance trade-off with any arbitrary prior imposition. As a remedy to both the issues mentioned above, we introduce an additional state space in the form of flexibly learnable latent priors, in the optimization objective of the WAEs. We implicitly learn the distribution of the latent prior jointly with the AE training, which not only makes the learning objective feasible but also facilitates operation on different points of the bias-variance curve. We show the efficacy of our model, called FlexAE, through several experiments on multiple datasets, and demonstrate that it is the new state-of-the-art for the AE based generative models

Improving Sequential Latent Variable Models with Autoregressive Flows

We propose an approach for improving sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving frame of reference, removing temporal correlations, and simplifying the modeling of higher-level dynamics. This technique provides a simple, general-purpose method for improving sequence modeling, with connections to existing and classical techniques. We demonstrate the proposed approach both with standalone flow-based models and as a component within sequential latent variable models. Results are presented on three benchmark video datasets, where autoregressive flow-based dynamics improve log-likelihood performance over baseline models. Finally, we illustrate the decorrelation and improved generalization properties of using flow-based dynamics

On the Necessity and Effectiveness of Learning the Prior of Variational Auto-Encoder

Using powerful posterior distributions is a popular approach to achieving better variational inference. However, recent works showed that the aggregated posterior may fail to match unit Gaussian prior, thus learning the prior becomes an alternative way to improve the lower-bound. In this paper, for the first time in the literature, we prove the necessity and effectiveness of learning the prior when aggregated posterior does not match unit Gaussian prior, analyze why this situation may happen, and propose a hypothesis that learning the prior may improve reconstruction loss, all of which are supported by our extensive experiment results. We show that using learned Real NVP prior and just one latent variable in VAE, we can achieve test NLL comparable to very deep state-of-the-art hierarchical VAE, outperforming many previous works with complex hierarchical VAE architectures

A Tutorial on Deep Latent Variable Models of Natural Language

There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence properties, while deep learning makes it possible to parameterize these conditional likelihoods with powerful function approximators. While these "deep latent variable" models provide a rich, flexible framework for modeling many real-world phenomena, difficulties exist: deep parameterizations of conditional likelihoods usually make posterior inference intractable, and latent variable objectives often complicate backpropagation by introducing points of non-differentiability. This tutorial explores these issues in depth through the lens of variational inference.Comment: EMNLP 2018 Tutoria

Predictive Coding, Variational Autoencoders, and Biological Connections

This paper reviews predictive coding, from theoretical neuroscience, and variational autoencoders, from machine learning, identifying the common origin and mathematical framework underlying both areas. As each area is prominent within its respective field, more firmly connecting these areas could prove useful in the dialogue between neuroscience and machine learning. After reviewing each area, we discuss two possible correspondences implied by this perspective: cortical pyramidal dendrites as analogous to (non-linear) deep networks and lateral inhibition as analogous to normalizing flows. These connections may provide new directions for further investigations in each field.Comment: NeurIPS NeuroAI Workshop, NAISys, Neural Computatio