Related papers: Semisupervised regression in latent structure netw…

We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to…

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…

In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum…

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the…

Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

Graph convolutional networks learn effective node embeddings that have proven to be useful in achieving high-accuracy prediction results in semi-supervised learning tasks, such as node classification. However, these networks suffer from the…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Graph attention networks (GATs) are widely used and often appear robust to noise in node covariates and edges, yet rigorous statistical guarantees demonstrating a provable advantage of GATs over non-attention graph neural networks~(GNNs)…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…

This paper presents a novel graph-based deep learning model for tasks involving relations between two nodes (edge-centric tasks), where the focus lies on predicting relationships and interactions between pairs of nodes rather than node…

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…