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Research on probabilistic models of networks now spans a wide variety of fields, including physics, sociology, biology, statistics, and machine learning. These efforts have produced a diverse ecology of models and methods. Despite this diversity, many of these models share a common underlying structure: pairwise interactions (edges) are generated with probability conditional on latent vertex attributes. Differences between models generally stem from different philosophical choices about how to learn from data or different empirically-motivated goals. The highly interdisciplinary nature of work on these generative models, however, has inhibited the development of a unified view of their similarities and differences. For instance, novel theoretical models and optimization techniques developed in machine learning are largely unknown within the social and biological sciences, which have instead emphasized model interpretability. Here, we describe a unified view of generative models for networks that draws together many of these disparate threads and highlights the fundamental similarities and differences that span these fields. We then describe a number of opportunities and challenges for future work that are revealed by this view.
Despite recent advances, the remaining bottlenecks in deep generative models are necessity of extensive training and difficulties with generalization from small number of training examples. We develop a new generative model called Generative Matching
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $eta$ that may take values either less than and greater than two. Models based on various forms of e
Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution represent
Most real-world networks are incompletely observed. Algorithms that can accurately predict which links are missing can dramatically speedup the collection of network data and improve the validity of network models. Many algorithms now exist for predi
Probabilistic generative models can be used for compression, denoising, inpainting, texture synthesis, semi-supervised learning, unsupervised feature learning, and other tasks. Given this wide range of applications, it is not surprising that a lot of