# Embracing the Blessing of Dimensionality in Factor Models

arXiv: https://arxiv.org/abs/1610.07697 · HTML: https://mlsanity.com/paper/1610.07697/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2016.

## Built on by (most cited first, 4 of 4)

- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Are Latent Factor Regression and Sparse Regression Adequate?](https://mlsanity.com/paper/2203.01219/) (2022)
- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [A Mathematical Framework for the Problem of Security for Cognition in Neurotechnology](https://mlsanity.com/paper/2403.07945/) (2024)

## Abstract (arXiv)

Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data is often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of targeted variables, shall we employ additional data, which are beyond the variables of interest, in the estimation? In this paper, we provide sufficient conditions for an affirmative answer, and further quantify its gain in terms of Fisher information and convergence rate. In fact, even an oracle-like result (as if all the factors were known) can be achieved when a sufficiently large number of variables is used. The idea of utilizing data as much as possible brings computational challenges. A divide-and-conquer algorithm is thus proposed to alleviate the computational burden, and also shown not to sacrifice any statistical accuracy in comparison with a pooled analysis. Simulation studies further confirm our advocacy for the use of full data, and demonstrate the effectiveness of the above algorithm. Our proposal is applied to a microarray data example that shows empirical benefits of using more data.