DeepAI
Log In Sign Up

Hyperbolic Graph Embedding with Enhanced Semi-Implicit Variational Inference

10/31/2020
by   Ali Lotfi Rezaabad, et al.
0

Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work we build off of semi-implicit graph variational auto-encoders to capture higher order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical variational Bayes to implicitly capture posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and highly correlated latent structures. We show that the existing semi-implicit variational inference objective provably reduces information in the observed graph. Based on this observation, we estimate and add an additional mutual information term to the semi-implicit variational inference learning objective to capture rich correlations arising between the input and latent spaces. We show that the inclusion of this regularization term in conjunction with the embedding boosts the quality of learned high-level representations and enables more flexible and faithful graphical modeling. We experimentally demonstrate that our approach outperforms existing graph variational auto-encoders both in Euclidean and in hyperbolic spaces for edge link prediction and node classification.

READ FULL TEXT
08/19/2019

Semi-Implicit Graph Variational Auto-Encoders

Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to ex...
08/26/2019

Variational Graph Recurrent Neural Networks

Representation learning over graph structured data has been mostly studi...
02/28/2017

Hierarchical Implicit Models and Likelihood-Free Variational Inference

Implicit probabilistic models are a flexible class of models defined by ...
02/15/2020

Latent Variable Modelling with Hyperbolic Normalizing Flows

The choice of approximate posterior distributions plays a central role i...
05/14/2019

Correlated Variational Auto-Encoders

Variational Auto-Encoders (VAEs) are capable of learning latent represen...
06/14/2019

Learning Correlated Latent Representations with Adaptive Priors

Variational Auto-Encoders (VAEs) have been widely applied for learning c...
01/15/2021

Efficient Semi-Implicit Variational Inference

In this paper, we propose CI-VI an efficient and scalable solver for sem...