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One of the most central questions in network science is: which nodes are most important? Often this question is answered using structural properties such as high connectedness or centrality in the network. However, static structural…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
An important question that often arises in the operation of networked systems is whether to collect the real-time data or to estimate them based on the previously collected data. Various factors should be taken into account such as how…
Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions amongst nodes. We…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
We introduce a model for random-walking nodes on a periodic lattice, where the dynamic interaction network is defined from local interactions and E randomly-added long-range links. With periodic states for nodes and an interaction rule of…
In machine learning, there is a fundamental trade-off between ease of optimization and expressive power. Neural Networks, in particular, have enormous expressive power and yet are notoriously challenging to train. The nature of that…
In this paper, a new framework to study weighed networks is introduced. The idea behind this methodology is to consider that each node of the network is an agent that desires to satisfy his/her preferences in an economic sense. Moreover,…
In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and…
As the penetration of distributed energy resources (DERs) increases, harnessing their flexibility becomes critical for power system operations. Virtual power plants (VPPs) offer a promising solution. However, most existing scheduling tools…
This article provides a selective review on the recent literature on econometric models of network formation. The survey starts with a brief exposition on basic concepts and tools for the statistical description of networks. I then offer a…
We introduce a general model for the balance-sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the…
A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…