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Register a new userBounded Information Rate Variational Autoencoders
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Daniel Braithwaite
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper introduces a new member of the family of Variational Autoencoders (VAE) that constrains the rate of information transferred by the latent layer. The latent layer is interpreted as a communication channel, the information rate of which is bound by imposing a pre-set signal-to-noise ratio. The new constraint subsumes the mutual information between the input and latent variables, combining naturally with the likelihood objective of the observed data as used in a conventional VAE. The resulting Bounded-Information-Rate Variational Autoencoder (BIR-VAE) provides a meaningful latent representation with an information resolution that can be specified directly in bits by the system designer. The rate constraint can be used to prevent overtraining, and the method naturally facilitates quantisation of the latent variables at the set rate. Our experiments confirm that the BIR-VAE has a meaningful latent representation and that its performance is at least as good as state-of-the-art competing algorithms, but with lower computational complexity.
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Although substantial efforts have been made to learn disentangled representations under the variational autoencoder (VAE) framework, the fundamental properties to the dynamics of learning of most VAE models still remain unknown and under-investigated. In this work, we first propose a novel learning objective, termed the principle-of-relevant-information variational autoencoder (PRI-VAE), to learn disentangled representations. We then present an information-theoretic perspective to analyze existing VAE models by inspecting the evolution of some critical information-theoretic quantities across training epochs. Our observations unveil some fundamental properties associated with VAEs. Empirical results also demonstrate the effectiveness of PRI-VAE on four benchmark data sets.
Variational Autoencoder is a scalable method for learning latent variable models of complex data. It employs a clear objective that can be easily optimized. However, it does not explicitly measure the quality of learned representations. We propose a Variational Mutual Information Maximization Framework for VAE to address this issue. It provides an objective that maximizes the mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent code and allows one to select particular components of it to be most informative with respect to the observations. On top of that, the proposed framework provides a way to evaluate mutual information between latent codes and observations for a fixed VAE model.
Learning interpretable and disentangled representations of data is a key topic in machine learning research. Variational Autoencoder (VAE) is a scalable method for learning directed latent variable models of complex data. It employs a clear and interpretable objective that can be easily optimized. However, this objective does not provide an explicit measure for the quality of latent variable representations which may result in their poor quality. We propose Variational Mutual Information Maximization Framework for VAE to address this issue. In comparison to other methods, it provides an explicit objective that maximizes lower bound on mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent variable and allows one to select particular components of it to be most informative with respect to the observations. On top of that, the proposed framework provides a way to evaluate mutual information between latent codes and observations for a fixed VAE model. We have conducted our experiments on VAE models with Gaussian and joint Gaussian and discrete latent variables. Our results illustrate that the proposed approach strengthens relationships between latent codes and observations and improves learned representations.
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.
Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed. However, for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks. In this work, we introduce a new model, the Gaussian Process (GP) Prior Variational Autoencoder (GPPVAE), to specifically address this issue. The GPPVAE aims to combine the power of VAEs with the ability to model correlations afforded by GP priors. To achieve efficient inference in this new class of models, we leverage structure in the covariance matrix, and introduce a new stochastic backpropagation strategy that allows for computing stochastic gradients in a distributed and low-memory fashion. We show that our method outperforms conditional VAEs (CVAEs) and an adaptation of standard VAEs in two image data applications.
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