A Julia package devoted to the statistical analysis of a latent (non sparse) high dimensional graphs. The data are assumed to come from a model with mean field interaction driven by the latent graph. Moreover, the model may incorporate a community structure for the nodes of the graph: one excitatory and one inhibitory community. The two objectives are:
- The estimation of the connectivity parameter of the latent graph (which is independent of the community).
- The detection of the two communities.
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Related articles :
- Chevallier, Löcherbach, Ost (2024) and Chevallier, Ost (2024): Discrete time data modeled via a binary Markov Chain. This model is fully covered by the package.
- Delattre, Fournier (2016) and Liu (2020) : Continuous time data modeled via a Hawkes process (Liu (2020) extends the first paper by considering partial observation). This model is not covered by the package for now, but is expected to. There is no community structure here.
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Documentation : https://jucheval.github.io/MeanFieldGraph.jl/
The folder examples contains all the material used to produce the figures in Chevallier, Löcherbach, Ost (2024) (folder CLO24/, the plots may differ a little bit because the files are newer than the article) and Chevallier, Ost (2024) (folder CO24/). The files named:
simulation_*.jlcontain the commands to produce the data used,plot_*.jlcontain the commands used to produce the plots (assuming that you have already simulated data in the folderdata).