# Factor-Adjusted Regularized Model Selection

arXiv: https://arxiv.org/abs/1612.08490 · HTML: https://mlsanity.com/paper/1612.08490/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2016.

## Built on by (most cited first, 9 of 9)

- [Are Latent Factor Regression and Sparse Regression Adequate?](https://mlsanity.com/paper/2203.01219/) (2022)
- [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)
- [Pre-processing with Orthogonal Decompositions for High-dimensional Explanatory Variables](https://mlsanity.com/paper/2106.09071/) (2021)
- [Feature Augmentations for High-Dimensional Learning](https://mlsanity.com/paper/2509.00232/) (2025)
- [Distributionally Robust Recovery of Omitted Factors from Forecast Residuals with Application to Interest Rate Risk Management](https://mlsanity.com/paper/2601.04608/) (2026)
- [MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis](https://mlsanity.com/paper/2606.30648/) (2026)
- [FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime](https://mlsanity.com/paper/2608.15408/) (2026)

## Abstract (arXiv)

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric studies, we consider the case where covariate dependence can be reduced through factor model, and propose a consistent strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By separating the latent factors from idiosyncratic components, we transform the problem from model selection with highly correlated covariates to that with weakly correlated variables. Model selection consistency as well as optimal rates of convergence are obtained under mild conditions. Numerical studies demonstrate the nice finite sample performance in terms of both model selection and out-of-sample prediction. Moreover, our method is flexible in a sense that it pays no price for weakly correlated and uncorrelated cases. Our method is applicable to a wide range of high dimensional sparse regression problems. An R-package FarmSelect is also provided for implementation.