This repository contains code for T-Rex, an expectation-maximization (EM) algorithm for robustly fitting a statistical factor model. It fits a factor model by solving the maximum likelihood estimation problem

$$ \begin{array}{r} \text{minimize} & \text{log det } (FF^T + D) + (n/m) \sum_{i=1}^m \log(x_i^T (FF^T + D)^{-1} x_i) \\ \end{array} $$

where the variables are the diagonal matrix $D \in \mathbf{R}^{n \times n}$ and $F \in \mathbf{R}^{n \times r}.$ For more information, see our paper.

First install the packages listed in 'requirements.txt'.

• To recreate Figure 1, run MSE_vs_samples.ipynb.
• To recreate Figure 2, run MSE_vs_samples.ipynb.
• To recreate Figure 3 and 4, run TRex_vs_Tyler.ipynb.
• To recreate Figure 5 and 6, run collect_face_data.py followed by plot_recovered_faces.py and plot_all_test_faces.py.

If you wish to cite this work you may use the following BibTex:

@article{Cederberg2025,
  title={T-Rex: Fitting a Robust Factor Model via Expectation-Maximization},
  author={Cederberg, Daniel},
  journal={arXiv preprint arXiv:2505.12117},
  year={2025}
}