# Dirichlet Process Prior for Student's t Graph Variational Autoencoders
## 2 Related Work  
Exploring the proper form of latent representation is an essential task for many representation learning applications. Moreover, we have seen that learning a prior of latent variables is indispensable to the VAE models. From the theoretical perspective, some recent studies demonstrate the necessity of learning VAE prior. Reference [35] highlighted the significance of the probability distribution of latent space by analyzing some variants of variational evidence lower bound objective (ELBO). Since it is necessary to complete the VAE optimization process by maximizing the ELBO, and this process is equivalent to minimizing the KL divergence between the variational posterior and prior of latent variables. Furthermore, Reference [36] illustrates the negative impact of applying a simple prior for VAE models. That is to say, it will result in few active latent variables, and finally produce over-regularized models with unpromising latent representation, which is not conducive to the tasks of presentation learning.  
Considering the importance of latent representation for carrying out various learning tasks, some models improved VAE from the perspective of the Gaussian distribution of latent variables, which is commonly used in most VAE models and their variants. Reference [37] elaborate that applying the nonparametric process to a neural network can automatically ascertain some critical parameters in the model, such as model capacity. They use the stick-breaking process to generate latent variables, and the Stick-Breaking VAE model is constructed by various parameterization methods. This model shows more discriminative ability of latent representation than Gaussian VAEs. Reference [4] replace the Gaussian distribution of latent variables in the traditional VAE models with a higher error-tolerant St distribution and apply the standard St distribution as a prior, and demonstrate that heavy-tailed latent variables can agrandze their flexibility when the data contains outliers. Nonetheless, only aggrandizing the tail thickness is far from enough to make the latent variables adapt to the dimension with sufficient flexibility and obtain ample prior knowledge to represent the data. Nonetheless, only enlarging the tail thickness is far from enough to make the latent variables adapt to the dimension with sufficient flexibility and obtain ample prior knowledge to represent the data. All the works mentioned above are used to deal with tasks related to image data, while we intend to do the presentation learning tasks on network data.  
There are also a few works that employ the DP prior. In [38], they focus on the task of various classification through learning logistic-regression methods, and they illustrate that the DP is helpful to learn the similarity between different classification tasks. The DP-GP-LVM (Dirichlet Process-Gaussian Process-Latent Variable Models) [39] algorithm presents a Bayesian nonparametric latent variable model, apply the Gaussian process prior and DP prior at the same time. More precisely, they are used for producing latent variables and learning structure, respectively. However, neither of these works has considered the application of DP prior to latent variables. Our model takes full advantage of DP as a nonparametric method in the adaptive dimension and facilitates the learning of appropriate representation for latent variables.