Network inference via process motifs

This repository contains:

• code for a method for fast network inference from time-series data
• code for producing the results and figures in "Network inference via process motifs" by Alice C Schwarze, Sara M. Ichinaga, and Bingni W. Brunton.

Quickstart

If you came here to get started on using LCCF and/or LCRC for network inference ASAP, here is a 3-step guide:

1. Install the package from Github via pip:

   pip install git+https://github.com/acuschwarze/network-inference-via-process-motifs.git

2. Add the following code snippet to the files in which you want to use LCCF and/or LCRC.

   import qspems

3. For a time-series data set TS given in the form of a 2d numpy array, you can now infer a network structure with m edges a given number of edges in one line:

    A = qspems.inf_via_LCCF(TS, m)
   

   or

    A = qspems.inf_via_LCRC(TS, m)
   

The 2d numpy array A is the adjacency matrix of the inferred directed, unweighted network. If you set num_edges to None, A is a weighted score matrix.

You can add the keyword argument max_lag to indicate if you expect any tranmission lags on edges. The default value max_lag=1 indicates that signals take exactly one time step to traverse an edge. Setting max_lag=2 indicates that you expect signals to traverse edges in either 1 or 2 steps. Larger values for max_lag are also possible. However, very large numbers (e.g., max_lag=100) may lead to long computation times.

Files explained

• qspems/qsPEMs.py is the lite version of our code library. It lets a user compute the pairwise edge measures LCCF and LCRC and infer networks from them. (The non-lite version (i.e., all other files in this repository) includes functions for comparing LCCF and LCRC to other pairwise edge measures, running parameter sweeps, and plotting results.)
• notebooks-figures/ includes jupyter notebooks for recreating the figures in our paper.
• notebooks-other/ includes notebooks that we used to explore some aspects of the stochastic difference model and/or our proposed inference methods. Specifically, it includes a notebook where we derive the simplified expressions for the correction factors $\alpha^{(LCCF)}$ and $\alpha^{(LCRC)}$.
• utils/ includes several function libraries that we have written to use in our notebooks.
• libs/ includes the function library curvygraph from a previous research project (). We use it here to create drawings of process motifs.
• data/ includes pre-calculated synthetic data that make it easy to recreate the figures in our paper. To recalculate the data for any figure, change load=True to load=False in the respective notebook before running it. To recalculate all data (which may take several days or weeks, depending on the available computing resources), delete all files in data/ before running the notebooks.

Dependencies

Python libraries available via pip and conda

dill, matplotlib, networkx, netrd, numpy, scipy, seaborn,

Other python libraries

curvygraph (included in libs)