# Robust high dimensional factor models with applications to statistical machine learning

arXiv: https://arxiv.org/abs/1808.03889 · HTML: https://mlsanity.com/paper/1808.03889/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2018.

## Built on by (most cited first, 13 of 13)

- [Model Editing as a Robust and Denoised variant of DPO: A Case Study on Toxicity](https://mlsanity.com/paper/2405.13967/) (2024)
- [On the Provable Advantage of Unsupervised Pretraining](https://mlsanity.com/paper/2303.01566/) (2023)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA](https://mlsanity.com/paper/2303.06198/) (2023)
- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)
- [Factor-Augmented Regularized Model for Hazard Regression](https://mlsanity.com/paper/2210.01067/) (2022)
- [Factor Adjusted Spectral Clustering for Mixture Models](https://mlsanity.com/paper/2408.12564/) (2024)
- [Classification of high-dimensional data with spiked covariance matrix structure](https://mlsanity.com/paper/2110.01950/) (2021)
- [A statistical framework for GWAS of high dimensional phenotypes using summary statistics, with application to metabolite GWAS](https://mlsanity.com/paper/2303.10221/) (2023)
- [Generalized Factor Neural Network Model for High-dimensional Regression](https://mlsanity.com/paper/2502.11310/) (2025)
- [T-Rex: Fitting a Robust Factor Model via Expectation-Maximization](https://mlsanity.com/paper/2505.12117/) (2025)
- [Enhancing Spectral Embedding through Robust and Flexible Knowledge Transfer in Electronic Health Records](https://mlsanity.com/paper/2606.11570/) (2026)

## Abstract (arXiv)

Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new challenges: high dimensionality, strong dependence among observed variables, heavy-tailed variables and heterogeneity. High-dimensional robust factor analysis serves as a powerful toolkit to conquer these challenges. This paper gives a selective overview on recent advance on high-dimensional factor models and their applications to statistics including Factor-Adjusted Robust Model selection (FarmSelect) and Factor-Adjusted Robust Multiple testing (FarmTest). We show that classical methods, especially principal component analysis (PCA), can be tailored to many new problems and provide powerful tools for statistical estimation and inference. We highlight PCA and its connections to matrix perturbation theory, robust statistics, random projection, false discovery rate, etc., and illustrate through several applications how insights from these fields yield solutions to modern challenges. We also present far-reaching connections between factor models and popular statistical learning problems, including network analysis and low-rank matrix recovery.