Related papers: Generalized linear models with low rank effects fo…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…

This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…

Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis…

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…

Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In…

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models…

Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high…

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-universal practice of assuming that a function, matrix, or tensor…

Oversampling is a common characteristic of data representing dynamic networks. It introduces noise into representations of dynamic networks, but there has been little work so far to compensate for it. Oversampling can affect the quality of…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…

In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…

Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a…

Network models are an increasingly popular way to abstract complex psychological phenomena. While the study of the structure of network models has led to many important insights, little attention is paid to how well they predict…

We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…