Testing and segmentation of joint and individual components in integrative multi-source factor models
Abstract
Disentangling shared (joint) structures from source-specific (individual) variations is a fundamental task in multi-source data integration. Existing joint-individual models often rely on computationally intensive optimization or loose spectral bounds, leading to suboptimal separation accuracy and poor scalability. In this paper, we propose the Multi-Source Sequential Alignment Test (MSSAT). MSSAT leverages the geometric observation that true joint components manifest as closely aligned score subspaces across different data sources. By deriving the asymptotic null distribution of our alignment statistic, we develop a rigorous, resampling-free sequential testing procedure to accurately estimate the joint rank. Extensive simulations and real data applications, including a TCGA multi-omics dataset, demonstrate that MSSAT achieves superior separation accuracy and substantially faster computation compared to competing methods.
Related
- A Counterfactual Framework for Estimating Infectious Disease Prevalence under Repeated Testing with Symptomatic and Contact-Tracing Components
- Sparse PCA with Multiple Components
- Selecting the number of components in PCA via random signflips
- Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
- Wandering exposed Julia components of rational maps
BibTeX
@misc{kim2026testing,
title = {{Testing and segmentation of joint and individual components in integrative multi-source factor models}},
author = {Kyoowon Kim and Sungkyu Jung},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01313},
eprint = {2610.01313},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01313},
}
RIS
TY - UNPB
TI - Testing and segmentation of joint and individual components in integrative multi-source factor models
AU - Kyoowon Kim
AU - Sungkyu Jung
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01313
UR - https://arxiv.org/abs/2610.01313
AB - Disentangling shared (joint) structures from source-specific (individual) variations is a fundamental task in multi-source data integration. Existing joint-individual models often rely on computationally intensive optimization or loose spectral bounds, leading to suboptimal separation accuracy and poor scalability. In this paper, we propose the Multi-Source Sequential Alignment Test (MSSAT). MSSAT leverages the geometric observation that true joint components manifest as closely aligned score subspaces across different data sources. By deriving the asymptotic null distribution of our alignment statistic, we develop a rigorous, resampling-free sequential testing procedure to accurately estimate the joint rank. Extensive simulations and real data applications, including a TCGA multi-omics dataset, demonstrate that MSSAT achieves superior separation accuracy and substantially faster computation compared to competing methods.
ER -