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This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks. Our result implies that the origin is…

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…

Neural networks are very successful tools in for example advanced classification. From a statistical point of view, fitting a neural network may be seen as a kind of regression, where we seek a function from the input space to a space of…

Graph neural networks (GNNs) have attracted much attention because of their excellent performance on tasks such as node classification. However, there is inadequate understanding on how and why GNNs work, especially for node representation…

Multilayer networks have been widely used to represent and analyze systems of interconnected entities where both the entities and their connections can be of different types. However, real multilayer networks can be difficult to analyze…

This paper proposes a logistic undirected network formation model which allows for assortative matching on observed individual characteristics and the presence of edge-wise fixed effects. We model the coefficients of observed…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…

Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. A single GNN layer typically consists of a feature transformation and a feature aggregation operation. The former normally uses…

Estimating causal effects from observational network data is a significant but challenging problem. Existing works in causal inference for observational network data lack an analysis of the generalization bound, which can theoretically…

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

Graph neural networks have been widely used for learning representations of nodes for many downstream tasks on graph data. Existing models were designed for the nodes on a single graph, which would not be able to utilize information across…

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…

Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the…

In this work, we aim to classify nodes of unstructured peer-to-peer networks with communication uncertainty, such as users of decentralized social networks. Graph Neural Networks (GNNs) are known to improve the accuracy of simple…

We introduce network with sub-networks, a neural network which its weight layers could be detached into sub-neural networks during inference. To develop weights and biases which could be inserted in both base and sub-neural networks,…