This repository supports the paper "Stochastic Gradient Descent Methods and Uncertainty Quantification in Extended CLSNA Models".

• simulation/: This directory includes main.ipynb and simulate_congress.ipynb. The main.ipynb notebook serves as the entry point for simulations with synthetic data. It simulates a dynamic network from the CLSNA model with a fixed number of members and fits the extended CLSNA model to the simulated data for inference. The simulate_congress.ipynb simulates a dynamic network with changing membership and fit the extended CLSNA model to the simulated data for inference.

• X/207/: Contains the 207.ipynb file, which is the primary script for analyzing Twitter congressional hashtag networks with 207 nodes. These nodes represent members who were consistently present throughout the study period.

• X/505/: Contains the 505.ipynb file, analyzing the same Twitter congressional hashtag networks, but includes all nodes recorded during the study.

• X/yearly/: This directory contains raw network data files named aggregated_network_hashtag_intersection_year***.csv. Additionally, the network_features.csv file provides metadata about the actors in the network.

• X/compare/: The entry point here is compare.ipynb, which plots the trajectory of the mean latent positions of the members of each party, comparing the model fitting result from the reduced dataset in 207.ipynb and the full dataset in 505.ipynb.

Each notebook (main.ipynb, simulate_congress.ipynb, 207.ipynb, and 505.ipynb) can be executed from top to bottom. They call helper functions and classes from utils.py and congress_utils.py. Each notebook follows a unified structure with three primary steps:

1. Initial CLSNA Model Fit: Start with a CLSNA model with a higher-dimensional space than the intended dimension. The model is then fitted, utilizing the first p principal components of the fitted latent position as the initial values for the next step.

2. Point Estimation: A model with the targeted dimension is fitted. The outputs are point estimations for model parameters.

3. Variance/Covariance Estimation: Perform variance/covariance estimation for the parameters of interest.

Each step is unified under an SGD approach and utilizes a unified nn.module class from the PyTorch autodifferentiation library, defined in utils.py and congress_utils.py.

To report bugs encountered while running the code, please contact Hancong Pan at [email protected].