# T-Rex: Fitting a Robust Factor Model via Expectation-Maximization

arXiv: https://arxiv.org/abs/2505.12117 · HTML: https://mlsanity.com/paper/2505.12117/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 69 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Heteroskedastic PCA: Algorithm, Optimality, and Applications](https://mlsanity.com/paper/1810.08316/) (2018)
- [An Overview of Robust Subspace Recovery](https://mlsanity.com/paper/1803.01013/) (2018)
- [Robust high dimensional factor models with applications to statistical machine learning](https://mlsanity.com/paper/1808.03889/) (2018)
- [Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms](https://mlsanity.com/paper/1407.3079/) (2014)
- [Rigorous Guarantees for Tyler's M-estimator via quantum expansion](https://mlsanity.com/paper/2002.00071/) (2020)
- [Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributions](https://mlsanity.com/paper/1506.05215/) (2015)
- [HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise](https://mlsanity.com/paper/2101.03468/) (2021)
- [Robust low-rank covariance matrix estimation with a general pattern of missing values](https://mlsanity.com/paper/2107.10505/) (2021)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion](https://mlsanity.com/paper/2404.11590/) (2024)
- [Shrinking the eigenvalues of M-estimators of covariance matrix](https://mlsanity.com/paper/2006.10005/) (2020)
- [Tyler's Covariance Matrix Estimator in Elliptical Models with Convex Structure](https://mlsanity.com/paper/1404.1935/) (2014)
- [Computation of the Maximum Likelihood estimator in low-rank Factor Analysis](https://mlsanity.com/paper/1801.05935/) (2018)
- [Frank-Wolfe-based Algorithms for Approximating Tyler's M-estimator](https://mlsanity.com/paper/2206.09370/) (2022)
- [Low-rank covariance matrix estimation for factor analysis in anisotropic noise: application to array processing and portfolio selection](https://mlsanity.com/paper/2304.08813/) (2023)

## Abstract (arXiv)

Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models - i.e., low-rank plus diagonal covariance structures - offer a powerful framework for modeling such structures. However, traditional methods for fitting statistical factor models, such as principal component analysis (PCA) or maximum likelihood estimation assuming the data is Gaussian, are highly sensitive to heavy tails and outliers in the observed data. In this paper, we propose a novel expectation-maximization (EM) algorithm for robustly fitting statistical factor models. Our approach is based on Tyler's M-estimator of the scatter matrix for an elliptical distribution, and consists of solving Tyler's maximum likelihood estimation problem while imposing a structural constraint that enforces the low-rank plus diagonal covariance structure. We present numerical experiments on both synthetic and real examples, demonstrating the robustness of our method for direction-of-arrival estimation in nonuniform noise and subspace recovery.