# Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors

arXiv: https://arxiv.org/abs/1908.01252 · HTML: https://mlsanity.com/paper/1908.01252/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [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 Adjusted Spectral Clustering for Mixture Models](https://mlsanity.com/paper/2408.12564/) (2024)
- [Generalized Factor Neural Network Model for High-dimensional Regression](https://mlsanity.com/paper/2502.11310/) (2025)
- [Feature Augmentations for High-Dimensional Learning](https://mlsanity.com/paper/2509.00232/) (2025)
- [MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis](https://mlsanity.com/paper/2606.30648/) (2026)
- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (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)

Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weak serial dependence, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases it is difficult to analyze the eigenvectors of the data matrix. To address this issue, we propose simple estimators of the latent factors using cross-sectional projections of the panel data, by weighted averages with pre-determined weights. These weights are chosen to diversify away the idiosyncratic components, resulting in "diversified factors". Because the projections are conducted cross-sectionally, they are robust to serial conditions, easy to analyze and work even for finite length of time series. We formally prove that this procedure is robust to over-estimating the number of factors, and illustrate it in several applications, including post-selection inference, big data forecasts, large covariance estimation and factor specification tests. We also recommend several choices for the diversified weights.