Discovering Latent Network Structure in Point Process Data

By Scott W. Linderman, Ryan P. Adams. International Conference on Machine Learning, 2014

295 citations recorded by the source corpus.

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines mutually-exciting point processes with random graph models. We show how the Poisson superposition principle enables an elegant auxiliary variable formulation and a fully-Bayesian, parallel inference algorithm. We evaluate this new model empirically on several datasets.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6597372b0eeadafbf421b9275397dee412a1ebd5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hawkes Processes in Finance (2015, methodology): “In [49], Linderman and Adams developed a probabilistic model that combines Hawkes processes with random graphs models, that they applied on S&P100 data.”
Online Optimization in Dynamic Environments (2013, methodology): “3 DMD with parametric additive dynamics Finally, we look at self-exciting point processes on connected networks [54, 55].”
UvA-DARE (Digital Academic Repository) Neural Relational Inference for Interacting Systems Neural Relational Inference for Interacting Systems (2018, unknown): “Another example from computational neuroscience is (Linderman et al., 2016; Linderman & Adams, 2014) where they infer interactions between neural spike trains.”
Doctor AI: Predicting Clinical Events via Recurrent Neural Networks (2015, background): “By excluding patients that made less than two visits, we were left with 263,706 patients who made on average 54.61 visits per person.”
On the Origins of Memes by Means of Fringe Web Communities (2018, methodology): “Aiming to capture the relationship between them, we use a statistical model known as Hawkes Processes [56, 57], which describes how events occur over time on a collection of processes.”
Transformer Hawkes Process (2020, methodology): “We propose an extension to THP that integrates these relational graphs (Borgatti et al., 2009; Linderman & Adams, 2014) into the self-attention module via a similarity metric among users.”
Online Convex Optimization in Dynamic Environments (2015, background): “We look at self-exciting point processes on connected networks [56], [57].”