skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: CHIP: A Hawkes process model for continuous-time networks with scalable and consistent estimation
In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data consist of timestamped relational events, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) generative model for such networks. We show that applying spectral clustering to an aggregated adjacency matrix constructed from the CHIP model provides consistent community detection for a growing number of nodes and time duration. We also develop consistent and computationally efficient estimators for the model parameters. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits than existing continuous-time network models on several real networks.  more » « less
Award ID(s):
1830547
PAR ID:
10280779
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Advances in neural information processing systems
Volume:
33
ISSN:
1049-5258
Page Range / eLocation ID:
16983-16996
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Proceedings of Machine Learning Research)
    The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 
    more » « less
  2. ; ; ; (, Journal of Complex Networks)
    Abstract Dynamic community detection provides a coherent description of network clusters over time, allowing one to track the growth and death of communities as the network evolves. However, modularity maximization, a popular method for performing multilayer community detection, requires the specification of an appropriate null network as well as resolution and interlayer coupling parameters. Importantly, the ability of the algorithm to accurately detect community evolution is dependent on the choice of these parameters. In functional temporal networks, where evolving communities reflect changing functional relationships between network nodes, it is especially important that the detected communities reflect any state changes of the system. Here, we present analytical work suggesting that a uniform null network provides improved sensitivity to the detection of small evolving communities in temporal networks with positive edge weights bounded above by 1, such as certain types of correlation networks. We then propose a method for increasing the sensitivity of modularity maximization to state changes in nodal dynamics by modelling self-identity links between layers based on the self-similarity of the network nodes between layers. This method is more appropriate for functional temporal networks from both a modelling and mathematical perspective, as it incorporates the dynamic nature of network nodes. We motivate our method based on applications in neuroscience where network nodes represent neurons and functional edges represent similarity of firing patterns in time. We show that in simulated data sets of neuronal spike trains, updating interlayer links based on the firing properties of the neurons provides superior community detection of evolving network structure when groups of neurons change their firing properties over time. Finally, we apply our method to experimental calcium imaging data that monitors the spiking activity of hundreds of neurons to track the evolution of neuronal communities during a state change from the awake to anaesthetized state. 
    more » « less
  3. ; ; ; (, Proceedings of the World Wide Web Conference)
    We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which discard a significant amount of information by aggregating events over time to form network snapshots. In this paper, we introduce a block point process model (BPPM) for continuous-time event-based dynamic networks. The BPPM is inspired by the well-known stochastic block model (SBM) for static networks. We show that networks generated by the BPPM follow an SBM in the limit of a growing number of nodes. We use this property to develop principled and efficient local search and variational inference procedures initialized by regularized spectral clustering. We fit BPPMs with exponential Hawkes processes to analyze several real network data sets, including a Facebook wall post network with over 3,500 nodes and 130,000 events. 
    more » « less
  4. ; (, Biometrika)
    Abstract Latent space models are often used to model network data by embedding a network’s nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing a class of latent space models we call generalized linear network eigenmodels that can model various edge types (binary, ordinal, nonnegative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. We propose a Bayesian approach to dimension selection for generalized linear network eigenmodels based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. We show that the model’s posterior is consistent and concentrates on low-dimensional models near the truth. We demonstrate our approach’s consistent dimension selection on simulated networks, and we use generalized linear network eigenmodels to study the effect of covariates on the formation of networks from biology, ecology, and economics and the existence of residual latent structure. 
    more » « less
  5. ; ; ; (, Proceedings of the 7th International Workshop on Energy Harvesting & Energy-Neutral Sensing Systems)
    Batteryless sensor nodes compute, sense, and communicate using only energy harvested from the ambient. These devices promise long maintenance free operation in hard to deploy scenarios, making them an attractive alternative to battery-powered wireless sensor networks. However, complications from frequent power failures due to unpredictable ambient energy stand in the way of robust network operation. Unlike continuously-powered systems, intermittently-powered batteryless nodes lose their time upon each reboot, along with all volatile memory, making synchronization and coordination difficult. In this paper, we consider the case where each batteryless sensor is equipped with a hourglass capacitor to estimate the elapsed time between power failures. Contrary to prior work that focused on providing a continuous notion of time for a single batteryless sensor, we consider a network of batteryless sensors and explore how to provide a network-wide, continuous, and synchronous notion of time. First, we build a mathematical model that represents the estimated time between power failures by using hourglass capacitors. This allowed us to simulate the local (and continuous) time of a single batteryless node. Second, we show--through simulations--the effect of hourglass capacitors and in turn the performance degradation of the state of the art synchronization protocol in wireless sensor networks in a network of batteryless devices. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email