# High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations

arXiv: https://arxiv.org/abs/2512.15684 · HTML: https://mlsanity.com/paper/2512.15684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 3 of 3)

- [Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering](https://mlsanity.com/paper/2102.12293/) (2021)
- [Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares](https://mlsanity.com/paper/2510.17561/) (2025)
- [A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation](https://mlsanity.com/paper/2402.03169/) (2024)

## Abstract (arXiv)

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its behavior in high-dimensional regimes remains limited. In this paper, we study a data integration model in which two high-dimensional data matrices share a low-rank common latent structure while also containing individual-specific components. We analyze the singular vectors of the associated cross-covariance matrix using tools from random matrix theory and derive asymptotic characterizations of the alignment between estimated and true latent directions. These results provide a quantitative explanation of the reconstruction performance of the PLS variant based on Singular Value Decomposition (PLS-SVD) and identify regimes where the method exhibits counter-intuitive or limiting behavior. Building on this analysis, we compare PLS-SVD with principal component analysis applied separately to each dataset and show its asymptotic superiority in detecting the common latent subspace. Overall, our results offer a comprehensive theoretical understanding of high-dimensional PLS-SVD, clarifying both its advantages and fundamental limitations.